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

Solution

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

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