Question:medium

In the figure below, the unknown side of the triangle is the diameter of the circle. What is the area of the unshaded region? (Figure not drawn to scale)

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A triangle inscribed in a circle with one side equal to the diameter is always right-angled at the opposite vertex (angle in a semicircle).
Updated On: Jul 21, 2026
  • \(125.50\pi\) sq.cm
  • \(134\pi\) sq.cm
  • \(156.25\pi\) sq.cm
  • \(162.50\pi\) sq.cm
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The Correct Option is C

Solution and Explanation

Step 1: Recognise the Pythagorean triple.
15 and 20 are 5 times the base triple 3 and 4 (\(5\times3=15,\ 5\times4=20\)), and the base triple's hypotenuse is 5, so this triangle's hypotenuse is \(5\times5=25\) cm.
Step 2: Use the circumradius property of a right triangle.
In any right triangle, the circumradius equals half the hypotenuse, so \(R = \frac{25}{2} = 12.5\) cm. Since the triangle is inscribed in the given circle, this circumradius is exactly the circle's radius.
Step 3: Compute the circle's area directly.
\(Area = \pi R^2 = \pi (12.5)^2 = 156.25\pi\) sq.cm.
Step 4: Confirm this is the unshaded area.
Since no part of the circle is hatched in the figure, this full circular area is the unshaded region asked for.\[\boxed{Unshaded\ area = 156.25\pi\ sq.cm}\]
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