NCERT Solutions For Class 10 Maths Chapter 10 Circles

 NCERT Solutions For Class 10 Maths Chapter 10 Circles

11. Prove that the parallelogram circumscribing a circle is a rhombus.

Solution:

ABCD is a parallelogram circumscribing a circle with centre O. 

`therefore` AB = CD, BC = AD

The lengths of tangents drawn from an external point to a circle are equal.

DR = DS----(i)

BP = BQ-----(ii)

CR = CQ----(iii)

AP = AS-----(iv)

Adding all the equations 

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

(BP + AP) + (DR + CR) = (CQ + BQ) + (DS + AS)

AB + CD = BC + AD

AB + AB = BC + BC `(∵ AB = CD, BC = AD)`

2AB = 2BC

`therefore` AB = BC 

AB = BC = CD = DA

`therefore` ABCD is a rhombus

12.  A `triangle`ABC is drawn to circumscribe a circle of radius 4 cm such that the segments BD and DC into which BC is divided by the point of contact D are of lengths 8 cm and 6 cm respectively. Find the sides AB and AC.

Solution: