The given question is a medium difficulty 2-mark question from the chapter Circles. Concept tested: Lenghts of tangents drawn to a circle from an external point. The question appeared in the 2016 CBSE class 10 board paper.

Question 7: A quadrilateral ABCD is drawn to circumscribe a circle, with centre 0, in such a way that the sides AB, BC, CD and DA touch the circle at the points P, Q, R and S respectively. Prove that AB + CD = BC + DA

online.maxtute.com

Circle Property

From an external point, two tangents can be drawn to a circle. Both these tangents will be equal in length.

AP and AS are equal tangents drawn from A. Let the measure of AP = AS ='a' units.

BP and BQ are equal tangents drawn from B. Let the measure of BP = BQ = 'b' units.

CQ and CR are equal tangents drawn from C. Let the measure of CQ = CR = 'c' units.

DR and DS are equal tangents drawn from D. Let the measure of DR = DS = 'd' units.

**LHS**: AB + CD = AP + PB + CR + RD

= a + b + c + d ............. (1)

**RHS**: BC + DA = BQ + QC + DS + SA

= b + c + d + a ............. (2)

(1) = (2)

∴ AB + CD = BC + DAClass 10 Maths

Register in 2 easy steps and

Start learning in 5 minutes!

CBSE Class 10 Maths - 2022

- Real Numbers Revision Class
- Polynomials Revision Videos
- Linear Equations Revision Class
- Quadratic Equations Revision Class
- Arithmetic Progressions Revision Video
- Triangles Revision
- Coordinate Geometry Revision
- Trigonometry Revision Class
- Appl of Trigonometry
- Circles Revision Class
- Areas Related to Circles Revision Videos

Copyrights © 2016 - 22 All Rights Reserved by Maxtute.com - An Ascent Education Initiative.

Privacy Policy | Terms & Conditions

**Mobile:** (91) 93822 48484

**WhatsApp:** WhatsApp Now

**Email:** learn@maxtute.com