In figure, from an external point $P$, two tangents $P Q$ and $P R$ are drawn to a circle of radius

Question

In figure, from an external point $P$, two tangents $P Q$ and $P R$ are drawn to a circle of radius 4 cm with centre $O$. If $\angle Q P R=90^{\circ}$, then length of $P Q$ is\

Professor PC Thomas Classes · Answer

(b): Join OR. We know that, tangent to a circle is ⟂ to radius at the point of contact.\ So, $O Q \perp P Q$ and $O R \perp P R$.\ Also, $\angle Q P R=90^{\circ}$\ Now, in quadrilateral OQPR,\ \ $\angle Q O R=360^{\circ}-\left(90^{\circ}+90^{\circ}+90^{\circ}ight)$ $$ =90^{\circ} 	ext { (By angle sum property of a quadrilateral) } $$ Now, $\angle P Q O=\angle Q O R=\angle O R P=\angle R P Q=90^{\circ}$\ Also, $P Q=P R$\ ( ∵ Tangents drawn from an external point are equal)\ $	herefore P Q O R$ is a square.\ Hence, $P Q=O Q=4 \mathrm{~cm}$\