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SUMMARY Theorem 1: The perpendicular from the centre of a circle to a chord bisects the chord. Theorem 2: There is one and only one circle passing through three given non-collinear points. Theorem 3: the angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circle. Theorem 4: Angles in same segment of a circle are equal. Theorem 5: angle in the semicircle is a right angle. Theorem 6: the sum of either pair of opposite angles of a cyclic quadrilateral is 180°. Theorem 7: Equal chords of a circle (or of congruent circles) are equidistant from the centre (or centers). Theorem 8: A tangent to a circle is perpendicular to the radius through the point of contact. Theorem 9: Lengths of two tangents drawn from an external point to a circle are equal. SECTION – I (OBJECTIVE) 1.
In a circle of radius 10 cm, the length of chord whose distance is 6 cm from the centre is: (A) 4 cm (B) 5 cm (C) 8 cm (D) 16 cm
2.
If a chord of length 8 cm is situated at a distance of 3 cm from centre, then the diameter of circle is: (A) 11cm (B)10cm (C) 12cm (D) 15cm
3.
In the given circle ABCD, O is the centre and ∠BDC = 42°. Then ∠ACB is equal to: (A) 48° (B) 45° (C) 42° (D) 60°
4.
In the given figure, ∠CAB = 80°, ∠ABC = 40°. The sum of ∠DAB + ∠ABD is equal to:
(A) 80° (B) 100° (C) 120° (D) 140° 5. In the given figure, if C is the centre of the circle and ∠PRC = 15° , then ∠QCR is equal to:
∠PQC = 25° and
(A) 40° (B) (B) 60° (C) (C) 80° (D) (D) 120° HURRY!! Visit our portal and get your NCERT Solutions UPDATED 2021-22. These all very essential for your exam preparation