Question

A quadrilateral ABCD is drawn to circumscribe a circle .If the sum of the length of sides AB + CD = 20 cm then, find the sum of the length of sides AD + BC.

• A. 10 cm
• B. 20 cm
• C. 40 cm
• D. 50 cm

Answer 1

The correct option is B

20 cm

From the figure we observe that,
DR = DS (Tangents on the circle from point D) … (i)

AP = AS (Tangents on the circle from point A) … (ii)

BP = BQ (Tangents on the circle from point B) … (iii)

CR = CQ (Tangents on the circle from point C) … (iv)

Adding all these equations,

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

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

$\Rightarrow$ CD + AB = AD + BC

So, sum of the length of sides AD +BC = 20 cm