Question

O1 and O2 are the centres of two congruent circles intersecting each other at point C and D. The line joining their centres intersects the circles in point A and B such that AB>O1O2.If CD=6cm and AB = 12 cm ,determine the radius of either circle. ​

Answer 1

The radius of either circle is 3.75 cm  

• From the figure below attached, it's clear that,
• O1 represents the circle 1 and O2 represents the circle 2.
• radius = O1C = O1D = O2C = O2C = O1A = O2B  
• Therefore, we have O1CO2D as a rhombus  
• As we know that the diagonal of rhombus are perpendicular bisector    
• So, CD ⊥ O1O2  and CD bisect O1O2 ,  
• Therefore $CM = \dfrac{CD}{2} = \dfrac{6}{2} = 3 cm$  
• $O1M = \dfrac{O1O2}{2} =\dfrac{AB - O1A - OB}{2} =\dfrac{ 12 - r- r}{ 2} = \dfrac{12 -2 r}{ 2}= (6 - r) cm$
• Now triangle O1MC  , we apply Pythagoras theorem , and get
• O1C^2 = O1M^2 + CM^2  , Substitute values , we get
• r^2 = ( 6 - r )^2 + 32
• r^2 = 36 + r^2 - 12r  + 9
• 12r  = 45
• r =  3.75
• So,  Radius of either circle  =  3.75 cm    

Answer 2

Answer:

Step-by-step explanation: