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Circles — Flashcards

NIOS · Class 10 · Maths

24 flashcards for Circles (NIOS Class 10 Maths) to test yourself on key terms and facts. Sample: "A chord of a circle is 10 cm long and its"

36 questions24 flashcards4 formulas & key relations5 concepts

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A comprehensive labeled diagram illustrating the various parts and terms associated with a circle, including center, radius, diameter, chord, arc (minor and major), sector, segment, interior, exterior
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24 Flashcards·
Radius from chord and distanceChord length from radius and distanceDistance from centre to chordDiameter-radius relationCircumference
Card 1Radius from chord and distance

A chord of a circle is 10 cm long and its perpendicular distance from the centre is 6 cm. Find the radius of the circle.

Answer

Step 1: Half of the chord = 10/2 = 5 cm. Step 2: Use OA^2 = OM^2 + AM^2. Step 3: r^2 = 6^2 + 5^2 = 36 + 25 = 61. Step 4: r = (61)^(1/2) cm. Answer: Radius = (61)^(1/2) cm.

Card 2Radius from chord and distance

A chord of a circle is 8 cm long and the perpendicular distance from the centre is 3 cm. Find the radius.

Answer

Step 1: Half of the chord = 8/2 = 4 cm. Step 2: Use OA^2 = OM^2 + AM^2. Step 3: r^2 = 3^2 + 4^2 = 9 + 16 = 25. Step 4: r = 5 cm. Answer: Radius = 5 cm.

Card 3Chord length from radius and distance

A chord is at a distance of 4 cm from the centre of a circle of radius 6 cm. Find the length of the chord.

Answer

Step 1: Draw the perpendicular from the centre to the chord. It bisects the chord. Step 2: Let half-chord = x cm. Step 3: Use OA^2 = OM^2 + AM^2. Step 4: 6^2 = 4^2 + x^2. Step 5: 36 = 16 + x^2. Step 6…

Card 4Radius from chord and distance

A chord is 14 cm long and its distance from the centre is 7 cm. Find the radius.

Answer

Step 1: Half-chord = 14/2 = 7 cm. Step 2: Use OA^2 = OM^2 + AM^2. Step 3: r^2 = 7^2 + 7^2 = 49 + 49 = 98. Step 4: r = (98)^(1/2) = 7(2)^(1/2) cm. Answer: Radius = 7(2)^(1/2) cm.

Card 5Distance from centre to chord

The radius of a circle is 5 cm and a chord is 6 cm long. Find the distance of the chord from the centre.

Answer

Step 1: Half-chord = 6/2 = 3 cm. Step 2: Use OA^2 = OM^2 + AM^2. Step 3: 5^2 = OM^2 + 3^2. Step 4: 25 = OM^2 + 9. Step 5: OM^2 = 16, so OM = 4 cm. Answer: Distance from centre = 4 cm.

Card 6Diameter-radius relation

When do you use d = 2r? Show one example.

Answer

Use d = 2r when the diameter or radius is given and the other needs to be found. Example: If r = 7 cm, Step 1: d = 2r Step 2: d = 2 x 7 = 14 cm Answer: Diameter = 14 cm.

Card 7Circumference

When do you use C = 2πr? Show one example.

Answer

Use C = 2πr when the radius of a circle is known and the circumference is needed. Example: If r = 7 cm, Step 1: C = 2πr Step 2: C = 2 x (22/7) x 7 Step 3: C = 44 cm Answer: Circumference = 44 cm.

Card 8Circumference

Find the circumference of a circle with diameter 22 cm.

Answer

Step 1: Use C/d = π. Step 2: C = πd Step 3: C = (22/7) x 22 Step 4: C = 484/7 cm Step 5: C ≈ 69.14 cm Answer: Circumference = 484/7 cm or about 69.14 cm.

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Frequently Asked Questions

What are the important topics in Circles for NIOS Class 10 Maths?
Key topics in Circles include Circle and Related Terms, Arcs, Semicircle, and Angle Measure, Concentric Circles and Congruent Circles, Important Theorems on Chords and Arcs. Study these first, then practise questions on each for the NIOS Class 10 board exam.
How many flashcards are available for Circles?
There are 24 flashcards for Circles covering key definitions, facts and ideas. A few sample cards are shown on this page.
How should I revise Circles for the NIOS Class 10 board exam?
Learn the core ideas first, then work through the 36 practice questions on Circles. 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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