Question

The base QY of the given triangle is half of the chord ZY. Also, one of the sides of the triangle passes through the center of the circle. Comment on the type of the triangle.

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

Answer 1

Answer: (B), (D)

Scalene triangle

Given: $QY=ZQ$
$\therefore Q$ is the midpoint of the chord $ZY.$

Also, QX passes through the center of the triangle.
$\therefore QX$ must be perpendicular to $ZY.$
$\Rightarrow \angle XQY={90}^o$

Hence, the given triangle is a right triangle.

Also, the length of $ZY$ is less than the diameter of the circle.
$\therefore QY$ is less than the radius of the circle.

However, the side $QX$ passes through the center and touches the circle.
$\therefore QX$ is more than the radius of the circle.

Hence, $QX$ and $QY$ are of different lengths.
We know that hypotenuse of a right triangle is the largest side.
$\therefore$ All the sides are of different lengths, which is a property of a scalene triangle.