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Eighth grade mathematics question bank
Solution: A, let the radius of the circle be X, tangent AC to E, tangent BC to D, tangent AB to F, as shown in figure (1), and also get the square OECD, AE=AF, BD=BF, then a-x+b-x=c, x =

a+b & amp; #8722; c

2

, so this option is wrong;

B, let AB be tangent to F, the radius o F the circle is Y, and connect O F, as shown in Figure (2).

Then △BCA∽△OFA, ∴

Belonging to

B.C.

=

Australian second-class honorary officer

ab blood type

y

a

=

b & amp#8722; y

c

The solution is: y=

abdominal muscle

a+c

, so this option is wrong;

C. connect OE, OD,

AC and BC tangent to e and d respectively,

∴∠OEC=∠ODC=∠C=90,

OE = OD,

∴ Quadrilateral OECD is a square,

∴OE=EC=CD=OD,

Let the radius of circle o be r,

∵OE∥BC,∴∠AOE=∠B,

∠∠AEO =∠0db,

∴△ODB∽△AEO,

Old English

Bachelor of science

=

Automatic exposure device

mean sea level

r

a & amp#8722; r

=

b & amp#8722; r

r

Solution: r=

abdominal muscle

a+b

, so this option is correct;

Points D and O connect three tangent points, from top to bottom: OD, OE, of; Let the radius of the circle be x;

It is easy to know that BD=BF, so AD = BD-BA = BF-BA = A+X-C;

∫b-x = AE = ad = a+x-c; So x=

b+ c & amp; #8722; a

2

, this option is wrong.

So choose C.

9.。 . . . . . .

Solution: extend BC and cross the x axis at point d,

Set point C(x, y), AB=a,

∵OC bisects the angle between OA and the positive semi-axis of the X axis,

∴cd=cb′,△ocd≌△ocb′,

From the nature of folding, BC=B'C,

∵ hyperbola y = 2 x? (x > 0) passes through the vertices a, c,

∴S△OCD= 1 2 xy= 1,

∴s△ocb′= 1 2xy = 1,

BC=B'C=CD can be obtained from the property of folding transformation and the equal distance between the point on the bisector of the angle and both sides of the angle.

∴ The vertical coordinates of point A and point B are both 2y,

∫AB∨x axis,

∴ point A(x-a, 2y),

∴2y(x-a)=2,

∴xy-ay= 1,

xy = 2

∴ay= 1,

∴S△ABC= 1 2 ay= 1 2,

∴soabc=s△ocb′+s△ab'c+s△abc= 1+ 1 2+ 1 ^ 2 = 2。

So the answer is: 2.