Question

In the given figure, quad. ABCD is circumscribed touching the circle at P, Q, R and S. If AP = 5 cm, BC= 7 c m and CS = 3 cm. Then, the length of AB = ?

(a) 9 cm 

(b) 10 cm 

(c) 12 cm 

(d) 8 cm

Answer 1

Correct answer is (a) 9 cm

Tangents drawn from an external point to a circle are equal.

So, AQ = AP = cm

CR = CS = 3cm

And BR = (BC - CR)

\(\Rightarrow\) BR = (7 - 3)cm

\(\Rightarrow\) BR = 4cm

BQ = BR = 4cm

∴ AB = (AQ + BQ)

\(\Rightarrow\) AB = (5 + 4)cm

\(\Rightarrow\) AB = 9cm