Question

If AB is a chord of a circle and P and Q are two points on the circle different from A and B, then:

• A. The angle subtended by AB at P and Q are either equal or supplementary.
• B. The sum of the angle subtended by AB at P and Q is always equal two right angle.
• C. The angle subtended at P and Q by AB are always equal.
• D. The sum of the angle subtended at P and Q is equal to four right angles

Answer 1

The correct option is A

The angle subtended by AB at P and Q are either equal or supplementary.

Since AB is a chord and P, Q are two points different from A and B, two cases arise:

Case 1: If P and Q are on the same side of the chord, angles subtended by the chords at P and Q are equal.

Case 2: If P and Q are on the opposite side of the chord, angles subtended by the chord are supplementary.