Question

In the figure, O is the centre of the circle. If $\angle$OBC = 25${}^{\circ }$, then $\angle$BAC in degree is equal to:

• A. 25
• B. 30
• C. 65
• D. 150

Answer 1

The correct option is C

65

OB=OC [radii of the same circle]

$\angle$OCB=$\angle$OBC=25${}^{\circ }$ [angles opposite to equal sides of a triangle]

So, $\angle$BOC = [180${}^{\circ }$-(25${}^{\circ }$+25${}^{\circ }$)] = 130${}^{\circ }$

$\therefore$ $\angle$BAC = $\frac{1}{2}$×$\angle$BOC = 65${}^{\circ }$

[The angle subtended by a chord at the centre of a circle is twice the angle subtended by the same chord at any other point on the remaining part of the circle.]