Question

A triangle has a side as diameter of a circle, and three of its vertices lie on the circle. What type of triangle is this?

• A. Acute triangle
• B. Right triangle
• C. Obtuse triangle

Answer 1

The correct option is B Right triangle

The angle subtended by the aiameter to any point on the circle is equal to ${90}^o.$

We know that the angle subtended by an arc at the centre of a cirlce is double the angle subtended by the arc at any point on the circle.

Here, the angle subtended by the arc AB at the centre is ${180}^o.$

$\therefore \angle ACB=\frac{{180}^o}{2}={90}^o$

A right triangle is a triangle whose one of the angles is ${90}^o.$
$\therefore △ABC$ is a right triangle.

Whereas, an acute triangle has all the angles as acute.
Hence, it is not an acute triangle.