Circles — Flashcards
Telangana Board · Class 9 · Mathematics
20 flashcards for Circles (Telangana Board Class 9 Mathematics) to test yourself on key terms and facts. Sample: "A circle has radius 7 cm. Find its"
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A circle has radius 7 cm. Find its circumference and area.
Answer
Step 1: Use circumference formula C = 2πr C = 2π(7) = 14π cm ≈ 44 cm Step 2: Use area formula A = πr² A = π(7)² = 49π cm² ≈ 154 cm² Answer: Circumference = 14π cm, Area = 49π cm²…
In a circle with center O, if chord AB = 8 cm and distance from center to chord is 3 cm, find the radius.
Answer
Step 1: Draw perpendicular OM from center O to chord AB Step 2: OM bisects AB, so AM = MB = 4 cm Step 3: In right triangle OAM: OA² = OM² + AM² OA² = 3² + 4² = 9 + 16 = 25 Step 4: OA = √25 = 5 cm Ans…
Two equal chords AB and CD of a circle subtend angles of 60° each at the center. If AB = 6 cm, find CD.
Answer
Step 1: Given AB and CD are equal chords Step 2: Equal chords subtend equal angles at center (Theorem) Step 3: Since ∠AOB = ∠COD = 60° and both are equal chords Step 4: Therefore AB = CD Answer: CD =…
Find the angle subtended by an arc at the center if it subtends 35° at a point on the circle.
Answer
Step 1: Use theorem - angle at center = 2 × angle at any point on circle Step 2: Let angle at center = θ Step 3: θ = 2 × 35° Step 4: θ = 70° Answer: Angle at center = 70°…
In a circle, if the angle in a semicircle is ∠APB where AB is diameter, find ∠APB.
Answer
Step 1: AB is diameter, so arc AB is a semicircle Step 2: Angle subtended by semicircle at center = 180° Step 3: Using theorem: angle at center = 2 × angle on circle Step 4: 180° = 2 × ∠APB Step 5: ∠A…
Two chords PQ and RS of a circle are equidistant from center O. If PQ = 8 cm, find RS.
Answer
Step 1: Chords equidistant from center are equal in length (Theorem) Step 2: Given: distance from O to PQ = distance from O to RS Step 3: Therefore PQ = RS Step 4: Since PQ = 8 cm Answer: RS = 8 cm…
In cyclic quadrilateral ABCD, if ∠A = 75°, find ∠C.
Answer
Step 1: In cyclic quadrilateral, opposite angles are supplementary Step 2: ∠A + ∠C = 180° Step 3: 75° + ∠C = 180° Step 4: ∠C = 180° - 75° = 105° Answer: ∠C = 105°…
Find the circumradius of triangle ABC where AB = 6 cm, BC = 8 cm, and AC = 10 cm.
Answer
Step 1: Check if triangle is right-angled: 6² + 8² = 36 + 64 = 100 = 10² Step 2: Yes, it's right-angled at B Step 3: For right triangle, circumradius R = hypotenuse/2 Step 4: R = AC/2 = 10/2 = 5 cm A…
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