Circles and Angles — Important Questions
Kerala Board · Class 10 · Mathematics
44 important questions from Circles and Angles for Kerala Board Class 10 Mathematics, with answers. Written for the board exams 2027.
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Important Questions from Circles and Angles
If an arc of a circle subtends an angle of 45° at a point on the circle, what is its central angle?
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90°
Step 1: Let the central angle be x°. Step 2: By inscribed angle theorem: inscribed angle = central angle ÷ 2. Step 3: 45° = x° ÷ 2. Step 4: x° = 45° × 2 = 90°.
Which of the following statements about angles in a circle are correct?
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Angle in a semicircle is 90°, Inscribed angle is half the central angle, Angles in the same segment are equal, Opposite angles of a cyclic quadrilateral sum to 180°
All statements except 'Central angle is half the inscribed angle' are correct. The correct relationship is that inscribed angle is half the central angle, not the reverse.
In a circle, two chords AB and CD intersect at point P inside the circle. If ∠APC = 80°, what is ∠APD?
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100°
Step 1: When two chords intersect inside a circle, adjacent angles are supplementary. Step 2: ∠APC + ∠APD = 180° (linear pair). Step 3: 80° + ∠APD = 180°. Step 4: ∠APD = 180° - 80° = 100°.
If a quadrilateral has opposite angles measuring 85° and 95°, is it a cyclic quadrilateral?
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Yes, because 85° + 95° = 180°
Step 1: For a quadrilateral to be cyclic, opposite angles must be supplementary. Step 2: Check: 85° + 95° = 180°. Step 3: Since opposite angles sum to 180°, the quadrilateral is cyclic.
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Sources & Official References
- Kerala Board of Public Examinations — keralapareekshabhavan.in
- National Education Policy 2020 — education.gov.in
Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.
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