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  • From an external point P, two 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 = 10 cm, find the perimeter of the triangle PCD.

From an external point P, two 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 = 10 cm, find the perimeter of the triangle PCD.

Answers (1)

In this figure
CE = CA         [\because  Tangents from an external point to a circle are equal in length]  
Similarly,
DE = DB and  PB = PA
Perimeter of DPCD
= PC + CD + PD
= PC + CE + ED + PD        (\because  CD = CE + ED)
= PC + CA + DB + PD       \begin{bmatrix} \because CE= CA & \\ ED= DB& \end{bmatrix} 
= PA + PB                          [\because  PC + CA = PA and DB + PD = PB]
 = PA + PA                              [\because  PB = PA]
 = 2PA
 = 2 × 10                                   [\because  PA = 10]
= 20 cm

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infoexpert27

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