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:
radius = d/2
Step-by-step explanation:
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Given :-
• O1 and O2 are the centres of two congruent circles intersecting at point C and D
• The line joining their centres intersect the circle at A and B such that AB > O1.O2
Solution :-
Here,
O1 represents the Circle 1 and O2 represents the circle 2
In the figure,
You can observed that ,
O1C = O1D = O2C = O2C = O1A = O2B
[ Radii of same circle ]
Therefore,
We have O1CO2D as a rhombus because its all sides are equal.
Now,
As we know that,
Diagonals of rhombus are perpendicular bisector
Therefore,
CD perpendicular to O1O2 and CD bisect O1O2
Therefore,
CM = CD/2 = 6/2 = 3cm
O1M = O1O2/2
= AB - O1A - OB / 2
= 12 - r - r / 2
= 12 - 2r/2
= ( 6 - r )cm
Now,
In traingle O1MC ,
By using Phythagores theorem
O1C^2 = O1MC^2 + CM^2
Subsitute values,
r^2 = ( 6 - r) ^2 + 32
r^2 = 36 + r^2 - 12r + 9
12r = 45
r = 3.75
Hence,
The radius of either circle is 3.75cm 
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