From an external point P, two tangents, PA and PB are drawn to a circle with centre O . At a point E on the circle, a tangent is drawn to intersect PA and PB at C and D, respectively. If PA = 10 cm, find the perimeter of ∆PCD

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Given PA = 10 cm We need to find perimeter of ∆PCD i.e. we need to find PC, PD and CD From Point A We know that Tangent from external point are equal ∴ PA = PB = 10 cm From Point C Since Tangent from external point are equal ∴ CA = CE From Point C Since Tangent from external point are equal ∴ DB = DE Now, Perimeter of ∆PCD = PC + PD + CD Putting CD = CE + ED = PC + PD + (CE + ED) Putting CE = AC, DE = DB = PC + PD + (AC + DB) = (PC + AC) + (PD + DB) = PA + PB = 10 + 10 = 20 cm

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.