Question

HOLA MATES! !!


ANSWER MUST BE IN COPY! !
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IF THE ANGLE BETWEEN TWO TANGENT DRAWN FROM AN EXTERNAL POINT P TO A CIRCLE OF RADIUS( a) AND CENTER O, IS 60.

THEN THE LENGTH OF OP.​

Answer 1

OA=a

OP=?

ANGLE BETWEEN TANGENTS=60°

Tangents are equally aligned to each other

=> <OPA=<OPB=30°

IN ∆OPA,

<POA=180°-90°-30°

=60°

Cos 60°=OA/OP

1/2 =a/OP

=> OP = 2a(Ans)

Answer 2

Angle APB = 60°

And Angle OPA = 30°

To find the length OP = ?

In triangle OPA :

Sin 30° = opposite/ hypotenuse = a/PO

1/2 = a/PO

∴ PO / OP = 2a.

So, the length of OP = 2a.