Question

A circle touches sides AB and AD of rectangle ABCD at P and Q respectively and passes through vertex C. If distance of C from chord PQ is 5 units, then area of rectangle is-

• A. 45
• B. 75
• C. 50
• D. 25

Answer 1

Answer: (D)

25

Answer 2

Let AB = a and CD = b which are along axes.

Let point C is (a, b)

Eq. of PQ is x + y = h

where (h, h) is centre of circle.

Distance of C from PQ

= $\frac{|a + b - h|}{\sqrt{2}}$ = 5

Ž a² + b² + h² + 2ab – 2ah – 2bh = 50 ......(1)

Also distance of C from centre

h = $\sqrt{(a - h)^{2} + (b - h)^{2}}$

Ž a² + b² – 2ah – 2bh + h² = 0 .......(2)

Solving (1) and (2) $\begin{matrix} ab = 25 \end{matrix}$