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)

Figure description: A circle with a marked centre. A horizontal chord through the centre (a diameter) forms the base of an inscribed triangle. The two slanted sides of the triangle, going from the two ends of this diameter up to a single apex point on the circle, are labelled 15 and 20. The third (unknown, horizontal) side of the triangle is the diameter of the circle itself. No portion of the figure is shaded/hatched.

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An angle inscribed in a semicircle is always 90 degrees, so use Pythagoras on the 15-20 legs to get the diameter first.
Updated On: Jul 20, 2026
  • 125.50π sq.cm
  • 134π sq.cm
  • 156.25π sq.cm
  • 162.50π sq.cm
  • 175 sq.cm
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The Correct Option is C

Solution and Explanation

The trick to this problem is recognising the special role of the diameter in a circle. Whenever a triangle is inscribed in a circle such that one of its sides is a diameter, the angle opposite that side (at the third vertex on the circle) is automatically 90 degrees. This is Thales' theorem, and it is exactly what lets us treat 15 and 20 as the two perpendicular legs of a right triangle.

Using the Pythagorean relation:
$$\text{hypotenuse}^2 = 15^2+20^2 = 225+400 = 625 \Rightarrow \text{hypotenuse} = 25$$

This hypotenuse is the diameter of the circle, so the radius is $r = 25/2 = 12.5$ cm.

The area enclosed by the circle is then:
$$A = \pi r^2 = \pi(12.5)^2 = 156.25\pi \text{ sq cm}$$

Since the diagram shows no shaded portion at all (it is a plain outline figure), the entire circular region counts as the unshaded area asked for in the question. So the answer is $\boxed{156.25\pi \text{ sq.cm}}$, option (c).
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