Question

What is the angle between the tangents if the corresponding radii are inclined at an angle of ${90}^{\circ }$?

• A. ${45}^{\circ }$
• B. ${90}^{\circ }$
• C. ${180}^{\circ }$
• D. $0^{\circ }$

Answer 1

The correct option is B ${90}^{\circ }$

Given radius inclined at 90${}^{\circ }$

so $\angle QOR={90}^{\circ }$

As It is seen from the figure,

Radius is perpendicular to the tangent (poperties of circle)

In quad. PQOR

$\angle P+\angle Q+\angle R+\angle S=360⟹\angle P+90+90+90=360⟹\angle P=360-270⟹\angle P={90}^{\circ }$

Hence Tangent inclined at ${90}^{\circ }$