Prove that the rectangle circumscribing a circle is a square.

Slide3.JPG

Slide4.JPG
Slide50.JPG

 

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

Check the answer here https://www.teachoo.com/1837/539/Ex-10.2--11---Prove-that-parallelogram-circumscribing-a-circle/category/Ex-10.2/

  1. Class 10
  2. Solutions of Sample Papers for Class 10 Boards

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

About the Author

Davneet Singh's photo - Teacher, Computer Engineer, Marketer
Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.