(\text{Two circles of radii 4 cm and 9 cm respectively touch each other externally at a point and a common tangent touches them at the points P and Q respectively. Then the area of a square with one side PQ is -} )
-
$\(72 \text{ cm}^2\)$
-
$\(144 \text{ cm}^2\)$
-
$\(97 \text{ cm}^2\)$
-
$\(194 \text{ cm}^2\)$
B
Correct answer
Explanation
For circles with radii 4 and 9 touching externally, distance between centers = 4+9 = 13. Length of common external tangent PQ = √(d² - (r₂-r₁)²) = √(13² - (9-4)²) = √(169-25) = √144 = 12. Area of square with side PQ = 12² = 144 cm².