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

Geometry
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?

- 24, 10
- 25, 9
- 24, 12
- 25, 10

### Answer

AC is the diameter and ∠ABC = 90°.

AC = 2 × 13 = 26 cm

In right angle triangle ABC,

AC^{2} = AB^{2} + BC^{2}

⇒ AB^{2} + BC^{2} = 26^{2}

⇒ AB^{2} + BC^{2} = 676

Now, you can check from the options.

Option A: 24^{2} + 10^{2} = 676

**The correct option is A.**