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:
Angle between the two radii OA and OB =Â 130$$^\circ$$
PA and PB are tangents at A and B to the circle
$$\Rightarrow$$ Â $$\angle $$OAP = 90$$^\circ$$ and $$\angle $$OBP =Â 90$$^\circ$$
In quadrilateral OAPB,
$$\angle $$OAP + $$\angle $$AOB + $$\angle $$OBP + $$\angle $$APB = 360$$^\circ$$
$$\Rightarrow$$Â 90$$^\circ$$ +Â 130$$^\circ$$ +Â 90$$^\circ$$ + $$\angle $$APB =Â 360$$^\circ$$
$$\Rightarrow$$ 310$$^\circ$$ +Â $$\angle $$APB =Â 360$$^\circ$$
$$\Rightarrow$$Â $$\angle $$APB =Â 50$$^\circ$$
$$\therefore\ $$Angle between the tangents =Â $$\angle $$APB = 50$$^\circ$$
Hence, the correct answer is Option A
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