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In the figure (ii) given below, from an external point P, tangents PA and PB are drawn to a circle. CE is a tangent to the circle at D. If AP = 15 cm, find the perimeter of the triangle PEC.

In the figure (ii) given below, from an external point P, tangents PA and PB are drawn to a circle. CE is a tangent to the circle at D. If AP = 15 cm, find the perimeter of the triangle PEC. Circles, ML Aggarwal Understanding Mathematics Solutions ICSE Class 10.

Circles

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Answer

From P, PA and PB are the tangents to the circle.

∴ PA = PB = 15 cm. (∵ if two tangents are drawn to a circle from an external point then the tangents have equal lengths.)

From E, EA and ED are the tangents to the circle.

∴ EA = ED (∵ if two tangents are drawn to a circle from an external point then the tangents have equal lengths.)

From C, BC and CD are the tangents to the circle.

∴ BC = CD (∵ if two tangents are drawn to a circle from an external point then the tangents have equal lengths.)

Now perimeter of triangle PEC,

=PE+EC+PC=PE+ED+CD+PC=PE+EA+CB+PC(ED=EA,CB=CD)=AP+PB=15+15=30 cm.= PE + EC + PC \\[1em] = PE + ED + CD + PC \\[1em] = PE + EA + CB + PC \\[1em] (\because \small{ED = EA, CB = CD}) \\[1em] = AP + PB \\[1em] = 15 + 15 \\[1em] = 30 \text{ cm}.

Hence, perimeter of triangle PEC = 30 cm.

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