Circle
ICSE · Class 9 · Mathematics
Most important questions from Circle for ICSE Class 9 Mathematics board exam 2026. MCQs, short answer, and long answer questions with marks.
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Which of the following statements about circles are correct?
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The perpendicular from center to chord bisects the chord, Equal chords are equidistant from center, All radii of a circle are equal
Statement 1: Theorem 23 states this. Statement 2: Theorem 24 proves this. Statement 4: By definition of circle. Statement 3 is wrong as diameter is the longest chord. Statement 5 is wrong as no chord can exceed diameter length.
Two chords AB and CD of a circle are parallel and lie on opposite sides of center. If AB = 16 cm, CD = 12 cm, and distance between chords is 14 cm, find the radius.
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10 cm
Let distances from center be x and (14-x). Half-lengths: 8 cm and 6 cm. From Pythagorean theorem: r² = x² + 8² and r² = (14-x)² + 6². Solving: x² + 64 = (14-x)² + 36. x = 6. So r² = 36 + 64 = 100, r = 10 cm.
Which of the following are properties of equal chords in a circle?
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They are equidistant from center, They subtend equal angles at center, They cut equal arcs
Equal chords have three main properties: (1) Equidistant from center (Theorem 24), (2) Subtend equal central angles, (3) Cut equal arcs. They don't need to pass through center or be parallel.
If arc AB = arc CD in a circle, what can we conclude about chords AB and CD?
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AB = CD
In a circle, equal arcs cut equal chords. This is a fundamental property: if arc AB = arc CD, then chord AB = chord CD.
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