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Circle — Flashcards

ICSE · Class 9 · Mathematics

24 flashcards for Circle (ICSE Class 9 Mathematics) to test yourself on key terms and facts. Sample: "Solve: A chord of length 6 cm is drawn"

37 questions24 flashcards2 formulas & key relations5 concepts

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A labeled diagram illustrating the fundamental components of a circle, including the center, radius, diameter, chord, and circumference.
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24 Flashcards·
Chord and distance from centreRadius from chord distanceChord length from radius and distanceRadius from chordComparing two chordsParallel chordsChord theorem
Card 1Chord and distance from centre

Solve: A chord of length 6 cm is drawn in a circle of radius 5 cm. Find the distance of the chord from the centre.

Answer

Step 1: Half of the chord = 6/2 = 3 cm. Step 2: Use OA² = OP² + AP². Step 3: 5² = OP² + 3². Step 4: 25 = OP² + 9. Step 5: OP² = 16, so OP = 4 cm. Answer: The distance from the centre is 4 cm.

Card 2Radius from chord distance

Solve: A chord of length 8 cm is at a distance of 3 cm from the centre. Find the radius of the circle.

Answer

Step 1: Half of the chord = 8/2 = 4 cm. Step 2: Use OA² = OP² + AP². Step 3: OA² = 3² + 4². Step 4: OA² = 9 + 16 = 25. Step 5: OA = 5 cm. Answer: The radius is 5 cm.

Card 3Chord length from radius and distance

Solve: The radius of a circle is 17 cm and the perpendicular from the centre to a chord is 8 cm. Find the length of the chord.

Answer

Step 1: Let half the chord be x cm. Step 2: Use OA² = OP² + AP². Step 3: 17² = 8² + x². Step 4: 289 = 64 + x². Step 5: x² = 225, so x = 15 cm. Step 6: Full chord = 2 × 15 = 30 cm. Answer: The chord is…

Card 4Radius from chord

Solve: A chord of length 24 cm is 5 cm from the centre. Find the radius of the circle.

Answer

Step 1: Half the chord = 24/2 = 12 cm. Step 2: Use OA² = OP² + AP². Step 3: r² = 5² + 12². Step 4: r² = 25 + 144 = 169. Step 5: r = 13 cm. Answer: The radius is 13 cm.

Card 5Comparing two chords

Solve: In the same circle, one chord is 24 cm long at a distance of 5 cm from the centre. Another chord is at a distance of 12 cm from the centre. Find the length of the second chord.

Answer

Step 1: From the first chord, half-length = 12 cm. Step 2: Radius = 13 cm from OA² = OP² + AP². Step 3: For the second chord, let half-length be x cm. Step 4: Use 13² = 12² + x². Step 5: 169 = 144 + x…

Card 6Parallel chords

Solve: Two parallel chords in a circle have lengths 30 cm and 16 cm. The radius is 17 cm. Find the distance between the chords when they are on opposite sides of the centre.

Answer

Step 1: For the 30 cm chord, half-length = 15 cm. Step 2: Distance from centre = √(17² - 15²) = √(289 - 225) = √64 = 8 cm. Step 3: For the 16 cm chord, half-length = 8 cm. Step 4: Distance from centre…

Card 7Parallel chords

Solve: Two parallel chords in a circle have lengths 30 cm and 16 cm. The radius is 17 cm. Find the distance between the chords when they are on the same side of the centre.

Answer

Step 1: Distance of the 30 cm chord from centre = 8 cm. Step 2: Distance of the 16 cm chord from centre = 15 cm. Step 3: On the same side, distance between chords = 15 - 8 = 7 cm. Answer: The distance…

Card 8Chord theorem

Why is a line from the centre that bisects a chord perpendicular to the chord?

Answer

Take the two triangles formed by joining the centre to the two ends of the chord and to its midpoint. Step 1: The two radii are equal. Step 2: The two halves of the chord are equal. Step 3: The shared…

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Frequently Asked Questions

What are the important topics in Circle for ICSE Class 9 Mathematics?
Key topics in Circle include Basic Ideas of a Circle, Position of Points and Types of Circles, Arc, Segment and Sector, Chord Theorems and Distance from the Centre. Study these first, then practise questions on each for Class 9 exams.
How many flashcards are available for Circle?
There are 24 flashcards for Circle covering key definitions, facts and ideas. A few sample cards are shown on this page.
How should I revise Circle for Class 9 exams?
Learn the core ideas first, then work through the 37 practice questions on Circle. Revise definitions regularly and use flashcards for quick recall before the exam.

Sources & Official References

Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.

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