Question

22.) Q and R is the centre of two congruent circles intersecting each other at point C and D the line joining their centre intersects the circles in the point A and B such that A and B do not lie between Q and R . if CD=6cm and AB=12cm, determine the radius of either circles and the distance between the centre of two circles?

Answer 1

For solutions, Refer to the attached picture.

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Let's see the related topics ;

☛ A circle is the locus of a point which moves in a plane in such a way that its distance from a given fixed point is always constant.

☛ A line segment joining the centre and a point on the circle is called its radius.

☛ The perimeter of a circle is called its circumference.

Circumference = 2 π r

☛ A chord of a circle is a line segment joining any two points on the circle.

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Answer 2

Heyy mate ❤✌✌❤

Here's your Answer. .

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Here
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 .
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