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 =12 cm find the perimeter of triangle pcd
Answers
★ CIRCLES ★
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 = 12 cm.
Lengths of tangents drawn from as external point to a circle are equal.
∴ PA = PB = 12 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
= 12 cm +
12 cm
= 24 cm.
Given : PA and PB are tangents to the circle drawn from an external point P. CD is the 3rd tangent touching the circle at Q. PA = 15cm
To Find : the perimeter of ⊿PCD.
Solution:
Perimeter of triangle PCD
PC + CD + PD
CD = CE + DE
=> Perimeter of triangle PCD = PC + CE + DE + PD
CE = CA Equal tangent
DE = DB Equal tangent
=> Perimeter of triangle PCD = PC + CA + DB + PD
PC + CA = PA
DB + PD = PB
=> Perimeter of triangle PCD = PA + PB
PA = PB Equal tangent
=> Perimeter of triangle PCD = PA + PA
=> Perimeter of triangle PCD = 2 * PA
PA = 15 cm
=> Perimeter of triangle PCD = 2 * 15 = 30 cm
Perimeter of triangle PCD = 30 cm
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