Question

O1 and O2 are the centers of two congruent circles intersecting at point C and D. The line joining their centers intersect the circle at A and B such that AB>O1 O2.If CD=6cm and AB=12cm,determine the radiUS of either circles.


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Answer 1

Answer:

3.75

O1C = O1D = O2C = O2C = O1A = O2B = r

And

From O1C = O1D = O2C = O2C ,

We get Quadrilateral O1CO2D is a rhombus .

And we know diagonal of rhombus are perpendicular bisector , So

CD ⊥O1O2 And CD bisect O1O2 , So

CP = CD2 = 62 = 3 cm

And

O1P = O1O22 =AB − O1A − OB2 = 12 − r − r2 = 12 −2 r2= (6 − r) cm

Now triangle O1PC , we apply Pythagoras theorem , and get

O1C2 = O1P2 + CP2 , Substitute values , we get

r2 = ( 6 - r )2 + 32

r2 = 36 + r2 - 12r + 9

12r = 45

r = 3.75

So,

Radius of either circle = 3.75 cm

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