Question

If tangents PA and PB from a point P to a circle with centre O are inclined to each other at

(a) 50°

(b) 60°

(c) 70°

(d) 80°

Answer 1

Let us first put the given data in the form of a diagram.

Given data is as follows:

We have to find.

We know that the radius of the circle will always be perpendicular to the tangent at the point of contact. Therefore,

Also, we know that sum of all angles of a quadrilateral will always be equal to 360°. Therefore in quadrilateral AOBP, we have,

Now consider ΔPOA and ΔPOB. We have,

PO is the common side for both the triangles.

PA = PB (Length of tangents drawn from the same external point will be equal)

OA = OB(Radii of the same circle)

Therefore, from SSS postulate of congruent triangles,

Therefore,

We have found that

That is,

Therefore, the correct answer is choice (a).