Question

AB is a chord, and O is the center of a circle. If ∠AOB is 78°, calculate the obtuse angle between AB and the tangent B.

a) 51°
b) 72°
c) 39°
d) 60°

Answer 1

The obtuse angle between chord AB and the tangent at point B, with ∠AOB equal to 78°, is found to be 51°.

Step-by-step explanation:

If AB is a chord, and O is the center of a circle with ∠AOB being 78°, we want to find the obtuse angle between chord AB and the tangent at point B. To do this, we remember the properties of a circle. The angle between a chord and a tangent at the point of contact is equal to the angle in the alternate segment, in this case, half of ∠AOB. So, the angle between AB and the tangent at B is half of 78°, which is 39°.

We can confirm this because the angle between a tangent and a radius drawn to the point of contact is 90° (a right angle); hence, if we subtract the acute angle between the chord AB and the radius OB (39°) from 90°, we get the required obtuse angle, which is also 51°. The correct answer is (a) 51°.