Question 63

If the angle between two radii of a circle be 130$$^\circ$$, then the angle between the tangents at the end of these radii (in degrees)is:

Solution

Angle between the two radii OA and OB = 130$$^\circ$$

PA and PB are tangents at A and B to the circle

$$\Rightarrow$$  $$\angle $$OAP = 90$$^\circ$$ and $$\angle $$OBP = 90$$^\circ$$

In quadrilateral OAPB,

$$\angle $$OAP + $$\angle $$AOB + $$\angle $$OBP + $$\angle $$APB = 360$$^\circ$$

$$\Rightarrow$$ 90$$^\circ$$ +  130$$^\circ$$ + 90$$^\circ$$ + $$\angle $$APB = 360$$^\circ$$

$$\Rightarrow$$ 310$$^\circ$$ + $$\angle $$APB = 360$$^\circ$$

$$\Rightarrow$$ $$\angle $$APB = 50$$^\circ$$

$$\therefore\ $$Angle between the tangents = $$\angle $$APB = 50$$^\circ$$

Hence, the correct answer is Option A


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