Question

A chord of a circle subtends 100 degree at a point on the minor arc.Find the angle it subtends at the centre.

Answer 1

$\Longrightarrow{\boxed{\bold{Answer: 200 \degree}}}$

$\textbf{\underline{Step-by-step explanation :- }}$

By theorem we know that,

The angle subtended at the center is twice the angle subtended at minor arc of circumference.

Mathematically, $ext. \angle AOB = 2 \angle ACB$

Now, angle at the center is ext. $\angle AOB$ while angle at minor arc is $\angle ACB$.

Since $\angle ACB = 100 \degree$

Therefore, $ext. \angle AOB = 2 × 100 \degree$

$\bold{\huge{\underline{ \angle AOB = 200 \degree}}}$