If tangents PA & PB from a point P to a circle with centre O are inclined to each other at an angle of 110º, then the   equal to :A 65º B 55º C 45º D  35º

The question seems to be incomplete. However, based on the given information, it seems like you are asking for the angle subtended by the tangents PA and PB at the center O of the circle.

In a circle, the angle subtended by a chord at the center is twice the angle subtended by it at any point on the alternate segment.

Here, PA and PB are tangents from an external point P and ∠APB is the angle between the tangents. According to the property, the angle subtended by the chord AB at the center O is twice of ∠APB.

So, ∠AOB = 2 * ∠APB

Given ∠APB = 110°

Therefore, ∠AOB = 2 * 110° = 220°

But in a circle, the maximum possible angle is 180°. So, the actual angle ∠AOB will be 360° - 220° = 140°

Now, the angle ∠AOB is subtended by the line segment OA and OB (radii of the circle). In a circle, the angle subtended by two radii is equal to the angle subtended by the arc or chord opposite to the angle.

So, ∠APB = ∠AOB = 140°

But the question seems to be asking for an angle that is either 65°, 55°, 45° or 35°. Without further information, it's not possible to determine which of these angles is being asked for.