Sarthaks Test
0 votes
12 views
in Circles by (9.0k points)
closed by

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?

1 Answer

+1 vote
by (9.2k points)
selected by
 
Best 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

Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students.

Categories

...