Circle — Important Questions
Maharashtra Board · Class 10 · Mathematics
44 important questions from Circle for Maharashtra Board Class 10 Mathematics, with answers. Written for the board exams 2027.
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Important Questions from Circle
Which of the following are properties of a cyclic quadrilateral? (Select all correct answers)
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Opposite angles are supplementary, External angle equals opposite interior angle, All vertices lie on the same circle
A cyclic quadrilateral has these key properties: (1) All vertices lie on the same circle (definition), (2) Opposite angles sum to 180°, and (3) An external angle equals the opposite interior angle. The other options are not necessarily true for all cyclic quadrilaterals.
In a circle with center O, two chords AB and CD intersect at point P inside the circle. If AP = 4 cm, PB = 6 cm, and CP = 3 cm, find PD.
A chord of length 16 cm is at a distance of 6 cm from the center of a circle. What is the radius of the circle?
An angle inscribed in a semicircle is always a right angle.
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True
This is true by Thales' theorem. An angle inscribed in a semicircle subtends an arc of 180°. By the inscribed angle theorem, the inscribed angle = (1/2) × 180° = 90°.
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