Let ABCD be a rectangle inscribed in a circle of radius 13 cm

Let ABCD be a rectangle inscribed in a circle of radius 13 cm. Which one of the following pairs can represent, in cm, the possible length and breadth of ABCD?

  1. 24, 10
  2. 25, 9
  3. 24, 12
  4. 25, 10

Answer

AC is the diameter and ∠ABC = 90°.

AC = 2 × 13 = 26 cm

In right angle triangle ABC,

AC2 = AB2 + BC2

⇒ AB2 + BC2 = 262

⇒ AB2 + BC2 = 676

Now, you can check from the options.

Option A: 242 + 102 = 676

The correct option is A.