Circles MCQs

Q1. On a Ferris wheel a steel chord is spanned by a rider on the far arc who measures it at 25 degrees. What angle does the same chord make at the centre?

• A.25 degrees
• B.65 degrees
• C.130 degrees
• D.50 degrees

Answer: D. 50 degrees

The central angle equals twice the angle at any point on the major arc. Central angle = 2 x 25 = 50 degrees.

Q2. A taut rope across a circular pond is sighted from the broad arc at 33 degrees by a boatman. Through what angle does this chord open at the centre of the circle?

• A.66 degrees
• B.33 degrees
• C.57 degrees
• D.114 degrees

Answer: A. 66 degrees

The central angle equals twice the angle at any point on the major arc. Central angle = 2 x 33 = 66 degrees.

Q3. Looking over a round dining table, a guest on the wide arc judges a string chord to be 41 degrees. What is the angle the chord subtends at the centre?

• A.98 degrees
• B.49 degrees
• C.41 degrees
• D.82 degrees

Answer: D. 82 degrees

The central angle equals twice the angle at any point on the major arc. Central angle = 2 x 41 = 82 degrees.