CBSE Class 10 Sample Paper for 2020 Boards - Maths Standard

Class 10
Solutions of Sample Papers for Class 10 Boards

Prove that the rectangle circumscribing a circle is a square.

Note : This is similar to Ex 10.2, 11 of NCERT – Chapter 10 Class 10

Transcript

Question 22 Prove that the rectangle circumscribing a circle is a square. Given: A circle with centre O. A rectangle ABCD touching the circle at points P, Q, R and S To prove: ABCD is a square Proof: A rectangle is a square with all sides equal, So, we have to prove all sides equal We know that 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 …(1) …(2) …(3) …(4) Since ABCD is a rectangle, Opposite sides are equal ∴ CD = AB & BC = AD AB + AB = AD + AD 2AB = 2AD AB = AD So, AB = AD & AB = CD & AD = BC So, AB = CD = AD = CD So, ABCD is a rectangle with all sides equal ∴ ABCD is a square Hence proved

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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, Social Science, Physics, Chemistry, Computer Science at Teachoo.