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Question

If the angle between two tangents drawn from an external point P to a circle of radius' a ' and centre O, the 60o the find the length of OP.


Solution

We know that tangent is always perpendicular to the radius at the point of contact.

So,                        OAP=900

We know that if 2 tangents are drawn from an external point, then they are equally inclined to the line segment joining the centre to that point.

 So  OPA=12APB=12×60=30

According to the angle sum property of triangle-

In AOP+OAP+OPA=180

AOP+90+30=180

AOP=60



So, AOP

tanAOP=APOA 

3=APa




therefore, AP = 3×a

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