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Please solve this question as early as possible.please |
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Answer» ,⇒ ∠B=90 o [ Given ]⇒ AB=12cm and AC=13cm [ Given ]Here, O is center of a circle and X is a radius.⇒ (AC) 2 =(AB) 2 +(BC) 2 [ By Pythagoras theorem ]⇒ (13) 2 =(12) 2 +(BC) 2 ⇒ 169=144+(BC) 2 ⇒ (BC) 2 =25∴ BC=5cmNow, AB,BC and CA are TANGENTS to the circle at P,N and M respectively.∴ OP=ON=OM=x [ Radius of a circle ]⇒ Area of △ABC= 21 ×BC×AB = 21 ×5×12 =30cm 2 Area of △ABC= Area of △OAB+ Area of △OBC+ Area of △OCA⇒ 30= 21 x×AB+ 21 x×BC+ 21 x×CA⇒ 30= 21 x(AB+BC+CA)⇒ x= AB+BC+CA2×30 ⇒ x= 12+5+1360 ⇒ x= 3060 ∴ x=2cm |
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