Question

Formula for angle between two tangents drawn to a circle in terms of cos

Answer 1

Answer:

Hi. Here's your answer:

Step-by-step explanation:

We know,

The tangents to a circle from an external point are equal.

So, AC=BC

Let the centre be O.

Then, AO=BO(radii of the same circle)

By theorem 10.1, ∠OAC=∠OBC=90°

Thus, in quadrilateral AOBC, ∠A=∠B=90°

We know, ∠A+∠B+∠C+∠O=360°

So, here we conclude that ∠O+∠C=180°_____________(∠O is the angle between two tangents i.e. AC and AB)

So,Formula for angle between two tangents=180°- central angle