Circles
NIOS · Class 10 · Maths
Flashcards for Circles — NIOS Class 10 Maths. Quick Q&A cards covering key concepts, definitions, and formulas.
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Get startedA 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.
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.
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…
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.
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.
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.
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.
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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