InterviewSolution
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InterviewSolution
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A circle is touching the side BC of a triangleABC at point P and touching AB and AC produced at Q and R respectively. Prove that AQ=(1)/(2)("perimeter of "triangle ABC). |
Answer» SOLUTION :Given : triangle ABC and a circle which touches BC, AB and AC in P,Q and R respectively. Proof : Since the length of the two tangents DRAWN from an external point to a circle are equal THEREFORE,  `AQ=AR""...(1)` `BQ=BP""...(2)` and `""CP=CR""...(3)` Now, PERIMETER of `triangle`ABC=AB+BC+AC `=AB+BP+PC+AC` `=AB+BQ+CR+AC""`[from (2) and (3)] `=AQ+AR=2AQ""`[from (1)] `:.""`Perimeter of `triangleABC=2AQ` `implies""AQ=(1)/(2)xx`(perimeter of `triangleABC`) HenceProved. |
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