**Question:**

In the given figure, a quadrilateral ABCD is drawn to circumscribe a circle such that its side AB, BC, CD and AD touch the circle at P, Q, R and S respectively. If AB = *x* cm, BC = 7 cm, CR = 3 cm and AS = 5 cm , find *x*

**Solution:**

We know that tangent segments to a circle from the same external point are congruent.

Now, we have

CR = CQ, AS = AP and BQ = BP

Now, BC = 7 cm

⇒ CQ + BQ = 7

⇒ BQ = 7 − CQ

⇒ BQ = 7 − 3 [∵ CQ = CR = 3]

⇒ BQ = 4 cm

Again, AB = AP + PB

= AP + BQ

= 5 + 4 [∵ AS = AP = 5]

= 9 cm

Hence, the value of *x* is 9 cm.