Question

In the figure a circle with center P

touches the semicircle at points Q

and C having center O. if diameter

AB = 10, AC = 6 then find the

radius of the smaller circle?​

Answer 1

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Solution:-

AP=AQ,BP and CR=CQ(tangents from external point)

perimeter of ∆ABC= AB +BR+RC+CA

=AB+BP = CQ+CA

= AP+AQ

=2AP

∆APO is a right angle triangle

AO^2=AP^2+PO^2

13^2=AP^2+5^2

AP^2=144

AP=12

Therefore perimeter of ∆ABC = 24 cm.

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