Tangents and Secants to a Circle
Telangana Board · Class 10 · Mathematics
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Quick Quiz: Tangents and Secants to a Circle
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A tangent PQ to a circle with center O and radius 5 cm meets a line through the center at point Q such that OQ = 13 cm. Find the length of PQ.
From an external point, two tangents PA and PB are drawn to a circle. If PA = 8 cm, find PB.
Calculate the length of tangent from a point 17 cm away from the center of a circle of radius 8 cm.
In a circle with center O, if two tangents from external point P make an angle of 60° with each other, and the radius is 6 cm, find the distance OP.
Sample Questions
Which of the following statements about tangents to a circle are correct?
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A tangent touches the circle at exactly one point, The tangent is perpendicular to the radius at point of contact, Two tangents can be drawn from any external point
A tangent touches circle at one point, is perpendicular to radius at contact point, and exactly two tangents exist from any external point. A tangent cannot pass through the center.
A quadrilateral ABCD circumscribes a circle. If AB = 8 cm, BC = 6 cm, and CD = 10 cm, find DA.
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12 cm
For a quadrilateral circumscribing a circle: AB + CD = BC + DA. Substituting: 8 + 10 = 6 + DA. Therefore 18 = 6 + DA, so DA = 12 cm.
Find the area of a sector with radius 7 cm and central angle 60°. (Use π = 22/7)
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77/3 cm²
Area of sector = (θ/360°) × πr². Substituting: Area = (60°/360°) × (22/7) × 7² = (1/6) × (22/7) × 49 = (1/6) × 22 × 7 = 154/6 = 77/3 cm².
A circle has radius 5 cm. Find the area of segment formed by a chord subtending 90° at center. (Use π = 22/7)
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275/14 - 25/2 cm²
Area of segment = Area of sector - Area of triangle. Sector area = (90°/360°) × π × 5² = (1/4) × (22/7) × 25 = 275/14 cm². Triangle area = (1/2) × 5 × 5 = 25/2 cm². Segment area = 275/14 - 25/2 cm².
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