Circles — Important Questions
Gujarat Board · Class 10 · Mathematics
42 important questions from Circles for Gujarat Board Class 10 Mathematics, with answers. Written for the board exams 2027.
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Important Questions from Circles
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, From an external point, exactly two tangents can be drawn, A tangent is perpendicular to the radius at the point of contact
The first three statements are fundamental properties of tangents. The fourth is incorrect because no tangent can be drawn from a point inside the circle.
From point P, tangents PA and PB are drawn to a circle. If ∠APB = 80°, what is ∠AOB where O is the center?
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100°
In quadrilateral PAOB, ∠OAP = ∠OBP = 90° (tangent perpendicular to radius). Sum of angles in quadrilateral = 360°. So ∠AOB = 360° - 90° - 90° - 80° = 100°.
A line is drawn at distance 5 cm from the center of a circle with radius 3 cm. How many points of intersection does the line have with the circle?
Which of the following distances from the center to a line would make the line tangent to a circle with radius 7 cm?
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7 cm, 7.0 cm
A line is tangent to a circle when the distance from the center to the line equals the radius. Since radius = 7 cm, the distance must be exactly 7 cm.
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