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CIRCLES and TANGENTS INTERSECTING CHORDS
Quiz by Rajashree Nambiar
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​AB is a chord of the circle and AOC is its diameter such that angle ACB = 50°. If AT is the tangent to the circle at the point A, then BAT is equal to ___(a) 65° (b) 60° (c) 50° (d) 40°
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​2)  If TP and TQ are the two tangents to a circle with centre O so that ∠POQ = 110°, then ∠PTQ is equal to ________________ (a) 60° (b) 70° (c) 80° (d) 90°
b
c
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AB is a chord of the circle and AOC is its diameter such that angle ACB = 50°. If AT is the tangent to the circle at the point A, then BAT is equal to ___(a) 65° (b) 60° (c) 50° (d) 40°
2)  If TP and TQ are the two tangents to a circle with centre O so that ∠POQ = 110°, then ∠PTQ is equal to ________________ (a) 60° (b) 70° (c) 80° (d) 90°
3) The length of a tangent from a point A at a distance 5 cm from the centre of the circle is 4 cm. The radius of the circle is: (a) 3 cm(b) 5 cm(c) 7 cm(d) 10 cm
In the figure below, the pair of tangents AP and AQ drawn from an external point A to a circle with centre O are perpendicular to each other and length of each tangent is 5 cm. Then the radius of the circle is_______________. (a) 10 cm (b) 7.5 cm (c) 5 cm (d) 2.5 cm
5) If two tangents inclined at an angle 60° are drawn to a circle of radius 3 cm, then length of each tangent is equal to _____(a) (3/2)√3 cm (b) 6 cm (c) 3 cm (d) 3√3 cm
6) In the figure below, PQ is a chord of a circle and PT is the tangent at P such that ∠QPT = 60°. Then ∠PRQ is equal to (a) 135° (b) 150° (c) 120° (d) 110°
7)  In the given figure, AB and AC are tangents to the circle with centre O such that ∠BAC = 40°, then ∠BOC is equal to [AI2011] (a) 40° (b) 50° (c) 140° (d) 150°
8) In the given figure, point P is 26 cm away from the centre O of a circle and the length PT of the tangent drawn from P to the circle is 24 cm. Then the radius of the circle is [Foreign 2011]Â (a) 25 cm(b) 26 cm(c) 24 cm (d) 10 cm
9) From a point P which is at a distance of 13 cm from the centre O of a circle of radius 5 cm, the pair of tangents PQ and PR to the circle are drawn. Then the area of the quadrilateral PQOR is ________ .(a) 60 cm²(b) 65 cm²c) 30 cm² (d) 32.5 cm²
10) In figure AT is a tangent to the circle with centre O such that OT = 4 cm and ∠OTA = 30°. Then AT is equal to ___________(a) 4 cm (b) 2 cm (c) 2√3 cm (d) 4√3 cm
11) In figure if O is centre of a circle, PQ is a chord and the tangent PR at P makes an angle of 50° with PQ, then ∠POQ is equal to [NCERT Exemplar Problems] (a) 100° (b) 80° (c) 90° (d) 75°
12) In figure, O is the centre of a circle, AB is a chord and AT is the tangent at A. If ∠AOB = 100°, then ∠BAT is equal to ______
(a) 100° (b) 40°(c) 50° (d) 90°
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20) If four sides of a quadrilateral ABCD are tangential to a circle, then_________
(a) AC + AD = BD + CD (b) AB + CD = BC + AD (c) AB + CD =AC + BC (d) AC + AD = BC + DBÂ Â Â Â