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Question
From an external point P, tangents PA and PB are drawn to a circle with centre O. At one point E on the circle tangent is drawn, which intersects PA and PB at C and D respectively. If PA=14cm, find the perimeter of ΔPCD.
From an external point P, tangents PA and PB are drawn to a circle with centre O. At one point E on the circle tangent is drawn, which intersects PA and PB at C and D respectively. If PA=14cm, find the perimeter of ΔPCD.
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Solution
PA and PB are tangent to the circle with center O. CD is a tangent to the circle at E, which intersect PA and PB in C and D respectively. The length of tangents drawn from an external point to a circle are equal.
PA = PB= 14 cm (given)
CA = CE
DB = DE
Perimeter of ΔPCD. = PC + CD + PD
= PC + (CE + ED) + PD
= PC + (CA + DB) + PD
= (PC + CA) + (DB + PD)
(CA = CE and DB= DE)
= PA + PB
= 14 cm + 14 cm
= 28 cm
Perimeter of ΔPCD. = 28 cm
PA and PB are tangent to the circle with center O. CD is a tangent to the circle at E, which intersect PA and PB in C and D respectively. The length of tangents drawn from an external point to a circle are equal.
PA = PB= 14 cm (given)
CA = CE
DB = DE
Perimeter of ΔPCD. = PC + CD + PD
= PC + (CE + ED) + PD
= PC + (CA + DB) + PD
= (PC + CA) + (DB + PD)
(CA = CE and DB= DE)
= PA + PB
= 14 cm + 14 cm
= 28 cm
Perimeter of ΔPCD. = 28 cm
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