Question

To draw a pair of tangents to a circle which are inclined to each other at an angle of ${45}^{\circ }$, it is required to draw tangents at end points of those two radii of the circle, the angle between them should be

• A. $135$
• B. $60$
• C. $45$
• D. $90$

Answer 1

The correct option is A $135$


In quad. $APBO$,
$\angle A=\angle B={90}^{\circ }$ (radius $\perp$ tangent)
$\angle A+\angle B+\angle P+\angle O={360}^{\circ }$
$\Rightarrow {90}^{\circ }+{90}^{\circ }+{45}^{\circ }+\angle 0={360}^{\circ }$
$\Rightarrow {225}^{\circ }+\angle 0={360}^{\circ }$
$\Rightarrow \angle 0={360}^{\circ }-{225}^{\circ }$
$\therefore \angle 0={135}^{\circ }$
$\Rightarrow x={135}^{\circ }$
$\Rightarrow$ Option (a).