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
Solution:
Given, PA and PB are the two tangents drawn to a circle with centre O though an external point P.
At point E on the circle the tangent is drawn which intersects PA and PB at C and D.
Given, PA = 10 cm
We have to find the perimeter of the triangle PCD.
We know that the tangents drawn to a circle through an external point are equal.
From the figure,
The tangents drawn through point P are PA and PB
So, PA = PB -------------- (1)
The tangents to the circle through C are CA and CE
So, CA = CE -------------- (2)
The tangents to the circle through D are DB = DE
So, DB = DE -------------- (3)
Considering triangle PCD,
Perimeter = PC + PD + CD
From the figure,
CD = CE + DE
So, perimeter = PC + PD + CE + DE
From (2) and (3),
Perimeter = PC + PD + CA + DB
On rearranging,
Perimeter = PC + CA + PD + DB
From the figure,
PC + CA = PA
PD + DB = PB
By (1), PA = PB
So, perimeter = PA + PB
Perimeter = PA + PA
= 2PA
Given, PA = 10 cm
So, 2PA = 2(10)
= 20 cm
Therefore, the perimeter of the triangle PCD is 20 cm.
✦ Try This: If tangents PA and PB from a point P to a circle with center O are drawn so that ∠APB = 80°, then, ∠POA?
☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 10
NCERT Exemplar Class 10 Maths Exercise 9.4 Problem 3
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
Summary:
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, the perimeter of the triangle PCD is 20 cm
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