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Question

From an external point P, tangents PA and PB are drawn to a circle with centre O. If CD is the tangent to the circle at a point E and PA = 14 cm, find the perimeter of ∆PCD.



Your Answer
A
14 cm
Your Answer
B
18 cm
Your Answer
C
24 cm
Correct Answer
D
28 cm

Solution

The correct option is D 28 cm

PA and PB are the tangents drawn from a point P outside the circle with centre O

CD is another tangent to the circle at point E which intersects PA and PB at C and D respectively.


 

PA = 14 cm

PA and PB are the tangents to the circle from P

PA = PB = 14 cm

Now CA and CE are the tangents from C

CA = CE ….(i)

Similarly DB and DE are the tangents from D

DB = DE ….(ii)

Now perimeter of ∆PCD

= PC + PD + CD

= PC + PD + CE + DE

= PC + CE + PD + DE

= PC + CA + PD + DB {From (i) and (ii)}

= PA + PB

= 14 + 14

= 28 cm

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