r be radius of incircle of triangle formed by joining centres of ( x − a ) 2 + ( y − b ) 2 = 9 , ( x − a ) 2 + ( y − b − 7 ) 2 = 16 and circle touching above two circles and having radius 5 units. Fin

Question

r be radius of incircle of triangle formed by joining centres of ( x − a ) 2 + ( y − b ) 2 = 9 , ( x − a ) 2 + ( y − b − 7 ) 2 = 16 and circle touching above two circles and having radius 5 units. Find r 2 .

TestHub · Accepted Answer

All three circles touch each other externally

$C_{1} C_{2} = 7$

$C_{2} C_{3} = 9$

$C_{3} C_{1} = 8$

$s = \frac{7 + 8 + 9}{2} = 12$

$Δ = s (s - a) (s - b) (s - c) = 12 \times 5 \times 3 \times 4$

$r = \frac{Δ}{s} = 5$

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