Question

Two tangents AB and AC are drawn to a circle with center O from the external point A. Prove that<BAC =2<OBC​

Answer 1

ok that's the answer pls follow

Answer 2

Hence proved that two tangents AB and AC are drawn to a circle with center O from the external point A is ∠BAC = 2∠OBC.

Given that,

From the exterior point A, two tangents, AB and AC, are drawn to a circle with the center O.

We have to prove ∠BAC = 2∠OBC

We know that,

In picture we can see the circle with tangent.

In triangle OAB

∠B=∠A=x

Then

∠O = 180°-2x

From kite ABOC

We get the angles as in quadrilateral sum of angle are equal to 360°

90°+90°+∠BOC+∠BAC =360°

180° +180°-2x+ ∠BAC=360°

∠BAC = 2x

∠BAC = 2∠OBC

Therefore, Hence proved that Two tangents AB and AC are drawn to a circle with center O from the external point A is ∠BAC = 2∠OBC.

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