Question

In the diagram, PQ is a tangent to the circle with center O, at P. QRS is a straight line. Find the value of $x$.

• A. $25$
• B. $35$
• C. $45$
• D. $75$

Answer 1

Answer: (B)

$35$

$\angle SRP=\frac{150}{2}={75}^0$ (angle at centre is twice the angle at the circumference)
$\therefore \angle PRQ=180-75={105}^0$
Join OR,
$\angle ORS={25}^0$
[since $OS=OR=Radius]$
$\angle ORP=75-25={50}^0$
$\angle OPR=\angle ORP={50}^0$
$[OR=OP=Radius]$
$\angle RPQ=90-50={40}^0[OP\perp PQ]$
$\angle RPQ+\angle PRQ+\angle RQP={180}^0$
$\angle RQP=180-[40+105]$
$=180-145$
$\therefore \angle RQP={35}^0$