Question

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

Answer 1

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

\(\Rightarrow\) CQ + BQ = 7

\(\Rightarrow\) BQ = 7 - CQ

\(\Rightarrow\) BQ = 7 - 3   [\(\because CQ = CR=3\)]

\(\Rightarrow\) BQ cm

Again, AP = BQ

= 5 + 4    [\(\because AS=AP=5\)]

= 9 cm

Hence, the value of x = 9cm