In Fig, PA and PB are tangents to the circle drawn from an external po

1.	In Fig, PA and PB are tangents to the circle drawn from an external point P. CD are a third tangent touching the circle at Q. If PB = 10 cm, what is the perimeter of Δ PCD?
Answer» Given: PB = 10 cm CQ = 2 cm Property: If two tangents are drawn to a circle from one external point, then their tangent segments (lines joining the external point and the points of tangency on circle) are equal. Using the above property, PA = PB = 10 cm (tangent from P) DB = DQ= 10 cm (tangent from D) And, CA = CQ= 10 cm (tangent from C) Now, Perimeter of ∆PCD = PC + CD + DP = PC + CQ + QD + DP = PC + CA + DB + PD [∵CA = CQ and DB = DQ] = PA + PB [∵PA = PC + CA and PB = PD + BD] = 10 cm + 10 cm = 20 cm Hence, Perimeter of ∆PCD = 20 cm

In Fig, PA and PB are tangents to the circle drawn from an external point P. CD are a third tangent touching the circle at Q. If PB = 10 cm, what is the perimeter of Δ PCD?

Answer»

Given:

PB = 10 cm

CQ = 2 cm

Property: If two tangents are drawn to a circle from one external point, then their tangent segments (lines joining the external point and the points of tangency on circle) are equal.

Using the above property,

PA = PB = 10 cm (tangent from P)

DB = DQ= 10 cm (tangent from D)

And,

CA = CQ= 10 cm (tangent from C)

Now,

Perimeter of ∆PCD = PC + CD + DP

= PC + CQ + QD + DP

= PC + CA + DB + PD [∵CA = CQ and DB = DQ]

= PA + PB [∵PA = PC + CA and PB = PD + BD]

= 10 cm + 10 cm

= 20 cm

Hence, Perimeter of ∆PCD = 20 cm

Discussion

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