Circles — Important Questions
Madhya Pradesh Board · Class 9 · Mathematics
43 important questions from Circles for Madhya Pradesh Board Class 9 Mathematics, with answers. Includes multiple choice and multiple correct questions.
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Important Questions from Circles
Which of the following are properties of equal chords in a circle?
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They subtend equal angles at the centre, They are equidistant from the centre, They form congruent arcs
Equal chords have multiple properties: they subtend equal angles at the centre (Theorem 9.1), are equidistant from the centre (Theorem 9.5), and form congruent arcs. They don't have different lengths (they're equal) and aren't necessarily parallel.
If the angle subtended by an arc at the centre is 80°, what is the angle subtended by the same arc at any point on the remaining part of the circle?
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40°
According to Theorem 9.7, the angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circle. So if the central angle is 80°, the inscribed angle is 80°/2 = 40°.
In a cyclic quadrilateral ABCD, if ∠A = 70°, what is ∠C?
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110°
In a cyclic quadrilateral, opposite angles are supplementary (sum to 180°). Since ∠A = 70°, we have ∠A + ∠C = 180°, so ∠C = 180° - 70° = 110°.
Two chords are equidistant from the centre of a circle. What can we conclude about these chords?
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They are equal in length
According to Theorem 9.6, chords equidistant from the centre of a circle are equal in length. This is the converse of the theorem that states equal chords are equidistant from the centre.
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