Class 10 Mathematics Circles: NCERT Solutions for Question 8

This page focuses on the detailed Circles question answers for Class 10 Mathematics Circles, addressing the question: 'A quadrilateral ABCD is drawn to circumscribe a circle (see Fig. 10.12). Prove that AB + CD = AD + BC '. The solution provides a thorough breakdown of the question, highlighting key concepts and approaches to arrive at the correct answer. This easy-to-understand explanation will help students develop better problem-solving skills, reinforcing their understanding of the chapter and aiding in exam preparation.
Question 8

A quadrilateral ABCD is drawn to circumscribe a circle (see Fig. 10.12). Prove that AB + CD = AD + BC

Given :  A quadrilateral ABCD which circumscribe a circle .

To prove: AB + CD = AD + BC

Proof: As we know tangents drawn from external point are equal. Therefore, we have

DR = DS                        …………….. (1)

AP = AS                        ……………… (2)

PB = BQ                        ……………… (3)

CR = CQ                       ………………. (4)

Adding equation (1), (2), (3) and (4), we get

DR + AP + PB + CQ = DS + AS + BQ + CR

AB + CD = AD + BC

Hence proved.