One of the diameter of the circle circumscribing the rectan…

Maths Circle and System of Circles Mix Single Correct MCQ

Published by: CGP EDU Academic Team

Published on: August 14, 2026

One of the diameter of the circle circumscribing the rectangle ABCD is 4y = x + 7.

If A and B are the points (–3, 4) and (5, 4) respectively, then the area of rectangle is-

40 sq. units

32 sq. units

30 sq. units

16 sq. units

Text Solution

Verified by Experts

The correct answer is:

First, we note that none of the points A (–3, 4) B(5, 4) lie on the diameter 4y = x + 7

Let E ( α, β ) be the centre of the circle,

then 4 β = α + 7 … (i)

Since ABCD is a rectangle |EA| = |EB| ⇒ EA 2 = EB 2

⇒ ( α + 3) 2 + ( β – 4) 2 = ( α –5) 2 + ( β –4) 2

⇒ 6 α + 9 = – 10 α + 25

⇒ α = 1, and from (i) β = 2

Now |AB| = = 8 and |BD| = 2|EB| = 2 =4

From right ∠ d Δ ABD, AD 2 = BD 2 –AB 2

= 80 –64 = 16

⇒ |AD| = 4,

∴ Area of the rectangle ABCD = |AB|. |AD|

= 8.4 = 32 sq. units.

Previous Question Next Question

Get practice questions, solutions, and test series in one place.

Share your experience with this question and solution.

Send your comment, doubt, correction, or feedback to admin.

What students say about this solution

No reviews yet. Be the first to write a review.