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(A) Given: Two tangents are drawn from an external point $A$ to the circle with centre $O$.$OA = 13\, cm$,radius $OP = OQ = 5\, cm$.Tangent $BC$ is dr

Vedclass · Accepted Answer

$24$

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(A) Given: Two tangents are drawn from an external point $A$ to the circle with centre $O$.$OA = 13\, cm$,radius $OP = OQ = 5\, cm$.Tangent $BC$ is drawn at a point $R$ on the minor arc $PQ$.To find: Perimeter of $	riangle ABC$.Proof: $\angle OPA = 90^{\circ}$ [Tangent at any point of a circle is perpendicular to the radius through the point of contact].In right-angled $	riangle OPA$,by Pythagoras theorem:$OA^2 = OP^2 + PA^2$$(13)^2 = 5^2 + PA^2$$169 = 25 + PA^2$$PA^2 = 144$$PA = 12\, cm$.Since tangents from an external point to a circle are equal in length,$AP = AQ = 12\, cm$.Also,$BP = BR$ and $CR = CQ$ (tangents from points $B$ and $C$ respectively).Perimeter of $	riangle ABC = AB + BC + CA$$= AB + (BR + RC) + CA$$= AB + BP + CQ + CA$$= (AB + BP) + (CQ + CA)$$= AP + AQ$$= 12 + 12 = 24\, cm$.

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