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CIRCLES
1. The angle in a semicircle measures:-
a. b. c. d.
45
0
60
0
90
0
36
0
2. An equilateral triangle of side 9 cm is inscribed in a circle. The radius of the circle is:-
a. 3cm b. c. d. 6cm
3 2 𝑐𝑚 3 3 𝑐𝑚
3. A chord is at a distance of 8cm from the center of a circle of radius 17cm. The length of
the chord is:-
a. 25cm b. 12.5cm c. 30cm d. 9cm
4. AB and CD are two equal chords of a circle the center O such that ∠AOB = . Then
80
𝑜
∠COD ?
a. b. c. d.
100
0
80
0
120
0
40
0
5. A chord is at a distance of 8 cm from the centre of a circle of radius 17 cm. The length of
the chord is
a. 25 cm b. 12.5 cm c. 30 cm d. 9cm
6. ABCD is a cyclic quadrilateral . If ∠DBC = , ∠BAC is , find ∠BCD.
80
𝑜
40
𝑜
7. A chord of a circle is equal to the radius of the circle. Find the angle subtended by the
chord at a point on the minor arc and also at a point on the major arc.
8. In the figure, O is the center of a circle, ∠AOC = and side AB has been produced to
110
𝑜
a point D. Find ∠CBD.
9. In Fig, ∠ ABC = 69°, ∠ ACB = 31°, find ∠ BDC.
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10. If the length of a chord of a circle at a distance of 24 cm from the center of the circle is
36 cm, find the length of the greatest chord of the circle.
11. Prove that equal chords of a circle subtend equal angles at the center.
12. Prove that the angle subtended by an arc at the center is double the angle subtended by
any point on the remaining part of the circle.
13. Prove that angles in the same segment of a circle are equal.
14. Prove that equal chords of a circle are equidistant from the centre.
15. Prove chords equidistant from the centre of a circle are equal in length.
