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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.
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.
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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
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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