Question

A chord of a circle is equal to its radius. The angle subtended by this chord at a point in major segment is

• A. ${60}^o$
• B. ${30}^o$
• C. ${120}^o$
• D. ${90}^o$

Answer 1

The correct option is B ${30}^o$

Given- PQ is the chord of a circle with centre O and $PQ=OP=OQ$.PQ subtends $\angle POQ$ & $\angle PRQ$ at the centre and at the cicumference.

To find out- $\angle PRQ=?$

Solution- $PQ=OP=OQ$.

$\therefore \Delta POQ$ is an equilateral one. So $\angle POQ={60}^o$. i.e $\angle PRQ=\frac{1}{2}\angle POQ=\frac{1}{2}\times {60}^o={30}^o.$ (The angle subtended by a chord at the centre of a circle is double of that at the cicumference.)

Ans- Option $B$