How to draw an inscribed square 5 inside a semicircle

Well, as you can imagine, it's actually equivalent to drawing an inscribed rectangle in a circle with a ratio of 1:2 on both sides, according to the Pythagorean theorem, the diagonal of this rectangle is the root number 5 (as opposed to 1:2), and the diagonal is twice the radius at the same time, which can be found according to the proportion

The last question for the day, good night

Oh, that's right, I took engineering drawing last semester, CAD is an elective content, only on the computer for half a day, this semester did not continue to repair the CAD drawing foundation, so that little fur can't help anything, but it won't be strict to the standard of ruler drawing, because ruler drawing has no scale. After calculating the length of one side, it is possible to cut it in the center on any diameter and then make the other two sides vertically, right? Hehe, I'm talking nonsense, because I'm not qualified to talk about CAD stuff right now, float away

Draw a circle first, then draw a right-angled triangle with a right-angled side of 1:2 (the right angle side is horizontal), then offset the hypotenuse of the triangle through the center of the circle, use the intersection of the offset line and the circle as an orthogonal line, and the four intersection points on the circle are connected together is the answer.

In this way: Let the side length of the square be x and the radius of the circle be r, then the formula should be satisfied: x 2+(x 2) 2=r 2 so that the side length of the inscribed square can be found.

Draw a rectangle with a 2:1 aspect ratio, circle it diagonally, and erase half of it

Roughly the same as dividing a circle into four equal parts is to find a 5 (1 2) side, which is difficult to describe.

Summary. How to draw a circle with a square inside: 1Draw a circle with the Geometry Artboard Circle tool, with the center of the circle as O, and use the Point tool to take any point A on the circle.

Select the points O and A, and select "Construction" - Line", and select the center of the circle O and Line Oa, and select "Construction" - Perpendicular Line". The intersection points of two lines and circles are a, b, c, and d.

Select points a, b, c, and d, and select "Construction" - Line Segment. Select two lines and press "Ctrl+H" to hide them. The circumscribed quadrilateral of the circle is drawn.

How to draw a circle with a square inside: 1Draw a circle with the Geometry Artboard Circle tool, with the center of the circle being o, and use the dot tool to take any point 2 on the circle

Select the points o and a, select "Construction" - straight line" for the model, select the center of the circle o and the line oa, select "Construction" - perpendicular line". The intersection points of the two straight lines and the circle are a, b, c, and 3Select points a, b, c, and d, and select "Construction" - Line Segment.

If you select a circle, you will also stare at the circle and hide it, and it will be drawn into a square. The above is the ** step of drawing the inner square of the circle on the geometric drawing board shared with you, let's learn and learn together. I believe it can help some new users.

Make a square diagonal, the distance from the intersection of the diagonal to the four vertices of the square is equal, this distance is the radius of the circumscribed circle, and the intersection of the diagonal is the center of the circumscribed circle. This is shown in the figure below.

The outer green circle is the circumscribed circle of the blue square in the diagram.

Method: State closure

1. Take the fixed length r as the radius to make the garden, pass the center of the circle O, and make the two vertical diameters of mn and hp in the vertical and horizontal.

2. Pass the point n to make a ray ns, take seven equal parts, connect the ms, and then pass the ns points to make the parallel lines of ms, and divide the mn seven parts.

3. Draw a circle with M as the center of the circle and Mn as the radius, and cross the HP extension line at the K point from the K point to the even or odd points (such as ) in the equinoxes of each equal point on the Mn Intersect the circle at the A, B, C, M points and then take AB, BC, CM as the side length, and start with a point (or M point) on the circle to cut off each once, and get the other three points connected in turn is the required regular heptagon.

A circle is surrounded by a regular polygon, which is a regular polygon with vertices all around the same circumference.

An important type of regular polygon is an important type of regular polygon within a circle. Refers to the vertices are all on the same circumference of the regular multi-mu banquet polygon, the regular polygon is always connected to the circle, so it is called the circle is connected to the regular polygon, and the circle is called the circumscribed circle of the regular polygon, therefore, the circle can be divided equally to obtain the regular polygon. That is, divide the circle into n(n)3) equal parts.

Connect the points in turn to get the inscribed n-sided shape of the circle. This circle is called the circumscribed circle of this regular n-sided shape, and when the number of sides n increases, the circumference of the circumscribed and circumscribed n-sided shapes of the circle approaches the circumference of the circle, and their area approaches the area of the circle. Greek and ancient Chinese mathematicians experienced this idea in line with modern limit theory, and both used it to calculate the crack resistance of the near-sail for pi.

The above information refers to the encyclopedia - circles are bordered by regular polygons.

If only a ruler is used to make a drawing, the circle is connected with a positive multi-sided hall. We can simply draw two types of inscribed regular polygons.

The first is to connect the square inside, making two parallel ambushes and searching for each other perpendicular diameter. Connect the four endpoints of the diameter in turn.

The second is to connect regular six polygons. Because the side length of the inscribed regular six polygons is exactly equal to the radius.

To these two basic graphs, we can continue to expand into regular 4x2 n-sided (8, 16, 32,......

or is a regular 3x2 n-sided (1,6,12,24......）

A semicircle is usableThe circle is surrounded by quadrilaterals

The number of the inner quadrilateral base car does not have to pass through the center of the circle, and does not have to exceed the semicircle, as long as the vertices of the quadrilateral are on the circle, the quadrilateral can be formed. The diagonal diagonal of the circumscribed quadrilateral of the circle is complementary. Because the arcs opposite the two inner angles form a circle, and the circumferential angles.

The degree is equal to half the degree of the opposite arc, which is half of the 360 degrees: 180°.

Arcs are represented by the symbol " ".

For example, an arc with a or b as the endpoint is read as arc ab or arc ab. Arcs larger than semi-circles are called superior arcs, and arcs smaller than semi-circles are called inferior arcs. The degree of an arc refers to the angle to which the arc is opposed.

degrees. The semicircle is also an arc, the straight line connecting the two points of AB is the chord AB, and the semicircle is neither an inferior arc nor an excellent arc, it is a boundary that distinguishes the inferior arc from the superior arc.

1. Definitions. 1. Circumscribed circle: The circle that intersects with each vertex of the polygon is called the circumscribed circle of the polygon, usually for a convex polygon, such as a triangle, if a circle happens to pass three vertices, the circle is called the circumscribed circle of the triangle, and the circle just surrounds the triangle.

2. Inscribed circle: In mathematics, if each side of a polygon on a two-dimensional plane can be tangent to a circle inside it, the circle is the inscribed circle of the polygon, and this polygon is called a circle inscribed polygon. It is also the largest circle inside a polygon.

The center of the inscribed circle is called the inner part of the polygon.

3. Inscribed circle: Usually for another circle, if a circle is inside another large circle, and the two circles have only one common point, this circle is called the inscribed circle of the great circle.

4. Inscribed circle: The inscribed circle is for another circle, if the two circles have only one common point, and the distance between the center of the circle is equal to the sum of the radii of the two circles, the two circles are inscribed circles to each other. When two circles are cut outward, there are 3 common tangent lines.

2. Drawing method.

1. Circumscribed circle: that is, the vertical bisector of the three sides of the triangle (two can also be used, and the intersection of the two lines determines one point).

Take a line segment as an example, which can be seen as one side of a triangle. Respectively, take the two endpoints as the center of the circle, the appropriate length (equal) as the radius to make a circle (only draw the arc that intersects with the line segment), and then take the two intersection points as the center of the circle, and the equal length as the radius (to ensure that the two circles intersect) to make a circle, and make a straight line at the two intersection points of the last two circles of Bu Chun, and the straight line is perpendicular and bisects this line segment, that is, the vertical bisector of the line segment.

2. Inscribed circle: In a triangle, the intersection of the angular bisector of the three corners is the center of the inscribed circle, and the perpendicular segments from the center of the circle to each side of the triangle are equal. A regular polygon must have an inscribed circle, and the center of its inscribed circle and the center of the circumscribed circle coincide, both in the center of the regular polygon.

3. Inner circle: The circle tangent to all three sides of the triangle is called the inscribed circle of the triangle, the center of the circle is called the inner of the triangle, and the triangle is called the inscribed triangle of the circle. The heart of the triangle is the intersection of the bisector of the three corners of the triangle.

4. Circumscribed circle: connect the center of the circle and the point outside the circle to the circle at one point, take this point and the point outside the circle as the radius, and draw the circle with the point outside the circle as the center of the circle.

III. Restrictions. 1. Circumscribed circles, triangles have circumscribed circles, and other figures do not necessarily have circumscribed circles. The circumscribed center of a triangle is the intersection of the perpendicular bisector on either side. The center of the triangle circumscribed circle is called the outer center.

2. The circle where the circumscribed circle intersects all the vertices of the polygon is called the circumscribed circle of the polygon. The geometry is within the circle, and its vertices are around the circumference.

3. Inscribed circle: A polygon has at most one inscribed circle, that is to say, for a polygon, its inscribed circle, if it exists, is the only one. Not all polygons have inscribed circles.

Triangles and regular polygons must have inscribed circles. A quadrilateral with an inscribed circle is called a circular circumscribed quadrilateral.

4. Inscribed circle, the triangle must have an inscribed circle, and other figures may not necessarily have an inscribed circle, and the center of the inscribed circle is fixed inside the triangle.

At any point on the circle o, draw an arc with a radius greater than the radius r and less than the diameter d, intersect with the circle at two points, connect the two points ab, do the perpendicular line of the calendar ab, draw an arc with the arc greater than half of the straight line with the center of the circle with the point a and b as the center of the circle to get two intersection points, and extend the intersection point through the center of the circle and the diameter is the diameter.

Connecting af, (extending) intersecting semicircles at g; Pass the point g as gh ab, hang the foot h; In order to intercept Hi=GH on AB, G, I are the center of the circle, GH is the radius as the arc, and the two arcs intersect at the point J, connecting GJ, IJ, and the square GHIJ is sought.

Determination theorem. 1: A diamond with an equal diagonal is a square.

2: There is a diamond with right angles that is an imaginary square.

3: Rectangles with diagonal perpendicular to each other are squares.

4: A set of rectangles with equal adjacent sides is a square.

5: A set of parallelograms with equal adjacent sides and one corner at right angles is a square.

1. Draw a circle with a compass on white paper, and the size of the circle is basically the size of a regular hexagon.

2. The radius of the compass does not need to be changed, find any point around the circle to make the center of the circle, and draw two arcs that coincide with the circle drawn before.

3. Draw the arc again at the place where the arc and the circumference intersect as the center of the circle and cross the circumference.

4. Draw six points that cross the circumference.

5. Connect the six points with a ruler, and our regular hexagon is drawn.