Ex 10.2, 8 - Chapter 10 Class 10 Circles

Last updated at April 16, 2024 by

Ex 10.2, 8 - A quadrilateral ABCD is drawn to circumscribe - Ex 10.2

Ex 10.2, 8 - Chapter 10 Class 10 Circles - Part 2

Go Ad-free

Transcript

Ex 10.2,8 A quadrilateral ABCD is drawn to circumscribe a circle (see figure). Prove that AB + CD = AD + BC Given : Let ABCD be the quadrilateral circumscribing the circle with centre O. The quadrilateral touches the circle at points P,Q,R and S To prove: AB + CD = AD + BC Proof: From theorem 10.2, lengths of tangents drawn from external point are equal Hence, AP = AS BP = BQ CR = CQ DR = DS Adding (1) + (2) + (3) + (4) AP + BP + CR + DR = AS + BQ + CQ + DS (AP + BP) + (CR + DR )= (AS + DS ) + (BQ + CQ) AB + CD = AD + BC Hence proved

Davneet Singh's photo - Co-founder, Teachoo

Made by

Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo