Circles — Flashcards
Karnataka Board · Class 9 · Mathematics
20 flashcards for Circles (Karnataka Board Class 9 Mathematics) to test yourself on key terms and facts. Sample: "Two equal chords AB and CD of a circle"
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Two equal chords AB and CD of a circle with center O subtend angles of 60° each at the center. If AB = 8 cm, find CD.
Answer
Step 1: Apply Theorem 9.1 - Equal chords subtend equal angles at center. Step 2: Since ∠AOB = ∠COD = 60° (given) Step 3: By the theorem, chords are equal when angles are equal Step 4: Therefore, CD = …
A chord PQ is 12 cm from the center of a circle with radius 13 cm. Find the length of the chord.
Answer
Step 1: Draw perpendicular OM from center O to chord PQ, OM = 12 cm Step 2: OM bisects PQ (perpendicular from center bisects chord) Step 3: In right triangle OMP: OP² = OM² + MP² Step 4: 13² = 12² + M…
In a circle, an arc subtends an angle of 80° at the center. What angle does it subtend at a point on the remaining part of the circle?
Answer
Step 1: Apply Theorem 9.7 - Angle at center = 2 × Angle at circumference Step 2: Let angle at circumference = θ Step 3: Angle at center = 2θ = 80° Step 4: Therefore, θ = 80°/2 = 40° Answer: The arc su…
PQRS is a cyclic quadrilateral. If ∠P = 70° and ∠Q = 80°, find ∠R and ∠S.
Answer
Step 1: Apply property of cyclic quadrilateral - opposite angles are supplementary Step 2: ∠P + ∠R = 180° and ∠Q + ∠S = 180° Step 3: Find ∠R: 70° + ∠R = 180° Step 4: ∠R = 180° - 70° = 110° Step 5: Fin…
Find the angle in a semicircle when a chord subtends it.
Answer
Step 1: In a semicircle, the arc is exactly half the circle Step 2: The angle subtended by diameter at center = 180° Step 3: Apply angle theorem: Angle at circumference = (1/2) × Angle at center Step …
Two chords AB and CD intersect inside a circle at point P. If ∠APD = 75°, find ∠BPC.
Answer
Step 1: When two chords intersect inside a circle, vertically opposite angles are equal Step 2: ∠APD and ∠BPC are vertically opposite angles Step 3: Therefore, ∠BPC = ∠APD Step 4: ∠BPC = 75° Alternati…
A chord of length 16 cm is at a distance of 6 cm from the center. Find the radius of the circle.
Answer
Step 1: Let O be center, AB be chord, OM be perpendicular from O to AB Step 2: OM = 6 cm (given), AB = 16 cm Step 3: OM bisects AB, so AM = MB = 16/2 = 8 cm Step 4: In right triangle OMA: OA² = OM² + …
When do you use the theorem 'Equal chords are equidistant from center'?
Answer
Use this theorem when: 1. You have two equal chords and need to find their distances from center 2. You know distances are equal and need to prove chords are equal Example: Chords AB = CD = 10 cm in a…
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Sources & Official References
- Karnataka SSLC — kseeb.kar.nic.in
- Dept of Pre-University Education, Karnataka
- National Education Policy 2020 — education.gov.in
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