Question:
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
Correct Answer: 1
We know that AC is the diameter and $\angle$ ABC = 90°. AC = 2*13 = 26 cm
In right angle triangle ABC,
$AC^2 = AB^2 + BC^2$
$\Rightarrow$ $AB^2+BC^2=26^2$
$\Rightarrow$ $AB^2+BC^2=676$
Let us check with the options.
Option (A): $24^2+10^2 = 676$.
Option (B): $25^2+9^2 = 706 \neq 676$.
Option (C): $25^2+10^2 = 725 \neq 676$.
Option (D): $24^2+12^2 = 720 \neq 676$.
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