The problem of the first three circles, the problem solving skills of the first three circles

are two answers.

Drawing. 1: AD and AC are on the same side of AB.

2: AD and AC are on the opposite side of AB.

1. First of all, it is necessary to flexibly mark and use the theorems and inferences introduced in the book, such as the vertical diameter theorem when you see the string and diameter, plus the complementary intersecting string theorem and the chord tangent angle theorem, these two are ideal for fill-in-the-blank selection, which can effectively improve the speed of solving problems, and I am interested in checking it.

2. If you have a big question, you can also use it directly. If the circle is generally used to find the isosceles triangle in the comprehensive problem, and the circle with the diameter as the side, the inner triangle is a right triangle, and the inner parallelogram is a rectangle, which is often used as an implicit obscuration condition. Combined with the known conditions informed by the question stem, a schematic diagram is drawn, and the known information and the information we deduce are marked in the diagram, so that we can make a one-step analysis and judgment of Hu Qing.

It's simple: connect EO

According to the theorem: the circumferential angle is equal to half of the central angle of the circle is concluded on Hu or have:

c= ∠d=

So c+ d= )

And because: aoe + boe = 180 degrees (this conclusion understands!) flat angle) so: c + d = 90 degrees.

It's over, let's simply destroy the mountain.

Analysis: This is used to accompany the circumferential angle of the same fox to be equal. Connecting ae, be, then eab= d, eba= c(same fox) eab+ eba=90° laughing pure c+ d=90°

The answer is 4.

The shortest chord is 8 and the longest is 10, one each.

There are 2 strings with a length of 9.

8 or 10 I** sent it.

1. If you connect to OD, then OD=OE=OB

So ode= oed

Because ed parallel oc

So ode= doc, oed= cob, od=ob, oc=oc

So odc obc

So odc obc

Because BC is the tangent and be is the diameter.

So ob vertical bc, i.e. obc=90

So odc=90, i.e., od is perpendicular dc, and od is the radius of the circle.

So cd is tangent to the circle o.

2. That is, AD is also tangent to the circle O.

So according to the cutting line theorem: AD2=ae*ab

ad=2, ae=1, so ab=4

So be=3, oe=3 2

Because de parallel oc

So ad dc=ae oe

So cd=ad*oe ae=(2*3 2) 1=3

Connect the OD

1）∵ed∥oc

deo=∠ceo

doc = boc = doe (circumferential corner, central corner) deo is positive

oe=odd on the circle o.

d is the tangent point. 2): Note: Similar, cut line learned the same as lksd1439 did not learn as follows:

Let od=x4+x=(x+1) (the Pythagorean theorem, where x can be reduced) to get x=, i.e., oe=od=

eb=3∴ab=4

cd=bc (tangent length).

Then set cd=k

k+2)²=k²+16

The solution is k=3, i.e., cd=3 is the result.

Needless to say, this is the most comprehensive and streamlined. Landlord plus points).

1.Connect od, because oe=od=ob, so angular oed=ode because oe parallel oc, so angular ode=doc, angular deo=cob

So the angle doc=cob, and because od=ob, oc=oc, so the triangle cdo is congruent with cbo, so the angle odc=90°, cd is the tangent of the circle o.

2.In the RT triangle AD2+OD2=AO2, AO=AE+EO, the solution is OD=3 2, and the same gives BC=3, so CD=3

I don't know if you can build a system (i.e., a Cartesian coordinate system).

If so, the process of the question is as follows.

Establish a Cartesian coordinate system with O as the origin and Ob as the X-axis.

then c(4,0).

Since OA is the origin and the slope k= 3 3 (according to the angle AOB = 30°), the straight line ao is y=(3 3)x

Because the circle c and oa have two different intersections, and oc=4, r 4

And the distance from point C to straight line OA should be r

Get 2 r to sum up 2 r 4