Question

the circle question please.. thanks

Answer 1

Hope it helps ya✌️✌️✌️✌️✌️✌️

Answer 2

Solution:

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Given:

A pair of tangents from an external point  to a circle inclined at an angle of 60°.

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To Prove :

The distance between the point from the center is equal to the diameter of the circle.

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Proof:

We know that

As per the diagram,

=> AB & AC are tangents to the given circle with center O,

=> OB is the distance between the point and the center of the circle.

So,
∡ABC = 60°,.

& OB bisects the angle ∡ABC into 2 equal angles ∡ABO & ∡ OBC.

∴ ∠ABO = 30°, ∠CBO = 30°,.

and if we join OA & OC,
we get,
 ∠ A & ∠C = 90° (Angle between radius of a circle and tangent is 90°)

Applying trigonometry on ΔABO,
we get,

sin 30° = $\frac{1}{2}$

$\frac{OA}{OB} = \frac{1}{2}$

2OA = OB,.

2 x radius of circle = OB,.

Diameter of circle = OB,.

Hence, proved.

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                                                 Hope it Helps!!

Diagram:
(sorry,I couldn't able to put this on top, and for low quality.)