From the external point P, tangents PA and PB are drawn to a circle with centre O. if CD is the tangents to the circle at a point E and PA=14cm, find the perimetre of triangle PCD.
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Given : PA and PB are tangent to the circle with centre O.
CD is a tangent to the circle at E which intersects PA and PB in C and D respectively and PA = 14 cm.
Lengths of tangents drawn from as external point to a circle are equal.
∴ PA = PB = 14 cm
CA = CE
DB = DE
Now perimeter of ΔPCD = PC + CD + PD
= PC + (CE + ED) + PD
= PC + (CA + DB) + PD
= (PC + CA) + (DB + PD)
= PA + PB
= 14 cm + 14 cm
= 28 cm.
CD is a tangent to the circle at E which intersects PA and PB in C and D respectively and PA = 14 cm.
Lengths of tangents drawn from as external point to a circle are equal.
∴ PA = PB = 14 cm
CA = CE
DB = DE
Now perimeter of ΔPCD = PC + CD + PD
= PC + (CE + ED) + PD
= PC + (CA + DB) + PD
= (PC + CA) + (DB + PD)
= PA + PB
= 14 cm + 14 cm
= 28 cm.
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