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Class 9 I'm Up and Down, and Round and Round worksheet
CBSE Mathematics. Circles: chords and their distance from the centre, angles at the centre and on the circle, cyclic quadrilaterals. Every sheet has 20 questions in three sections and an answer key, and the numbers change every time.
Sample questions
Real questions from this chapter, as the app sets them. Tap Answer to see the answer and working.
Section A · multiple choice
- 1.
O is the centre of a circle, and A, B, C are points on it. If ∠AOB = 70°, then ∠ACB (C on the major arc) is:
- 70°
- 35°
- 140°
- 145°
Answer
(b) 35°
the angle at the centre is double the angle at the circle: 70 ÷ 2
- 2.
AB is a diameter of a circle and C is a point on the circle. If ∠CAB = 71°, then ∠CBA is:
- 19°
- 161°
- 109°
- 71°
Answer
(a) 19°
∠ACB = 90° (angle in a semicircle); ∠CBA = 90° − 71°
- 3.
ABCD is a cyclic quadrilateral with ∠A = 140°. Then ∠C is:
- 40°
- 140°
- 220°
- 50°
Answer
(a) 40°
opposite angles of a cyclic quadrilateral add up to 180°
Section B · short answer
- 4.
In cyclic quadrilateral ABCD, ∠A = (2x − 1)° and ∠C = (5x − 57)°. Find x and both angles.
Answer
x = 34; ∠A = 67°, ∠C = 113°
∠A + ∠C = 180°: 7x − 58 = 180
- 5.
In cyclic quadrilateral ABCD, ∠A = 53° and ∠B = 97°. Find ∠C and ∠D.
Answer
∠C = 127°, ∠D = 83°
opposite angles add up to 180°
Section C · long answer
- 6.
A straight path 256 m long cuts across a circular park of radius 160 m, with both ends on the boundary. How far is the path from the centre of the park?
Answer
96 m
√(160² − 128²) = 96
Fresh sheets for your child
In the app, every I'm Up and Down, and Round and Round sheet is new: the app remembers the questions your child has already had and leaves them out. Print the sheet as a PDF, or use notebook mode and write the answers in a notebook.
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