Circles and Angles — Flashcards
Kerala Board · Class 10 · Mathematics
20 flashcards for Circles and Angles (Kerala Board Class 10 Mathematics) to test yourself on key terms and facts.
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What is the relationship between an inscribed angle and the central angle subtending the same arc?
Answer
The inscribed angle is half the central angle subtending the same arc. Formula: Inscribed angle = (1/2) × Central angle Example: If central angle = 120°, then inscribed angle = 60° This relationshi…
If you want to mark 1/3 of a circle using an angle from a point on the circle, what angle should you use?
Answer
You should use a 60° angle. Step-by-step reasoning: 1. 1/3 of circle = central angle of 120° 2. Using the inscribed angle theorem: inscribed angle = (1/2) × central angle 3. Required inscribed angle …
What is the measure of an angle inscribed in a semicircle?
Answer
An angle inscribed in a semicircle is always 90° (a right angle). Proof: - Semicircle has central angle = 180° - Inscribed angle = (1/2) × 180° = 90° This is known as Thales' theorem and is very use…
Problem: An arc subtends a central angle of 80°. What angle does it make at a point on the major arc?
Answer
The angle at a point on the major arc = 40° Solution steps: 1. Given: Central angle = 80° 2. The point is on the circle but not on the arc (on major arc) 3. Apply inscribed angle theorem: Inscribed a…
What are alternate arcs and how do angles in alternate arcs relate?
Answer
Alternate arcs: Two arcs formed when any two points divide a circle. Key relationships: 1. Angles inscribed in the same arc are equal 2. Sum of angles inscribed in alternate arcs = 180° Example: If …
Define a cyclic quadrilateral and state its main property.
Answer
Cyclic Quadrilateral: A quadrilateral whose all four vertices lie on a circle. Main Property: Sum of opposite angles = 180° Formally: ∠A + ∠C = 180° and ∠B + ∠D = 180° Converse: If sum of opposite …
Problem: In a cyclic quadrilateral ABCD, ∠A = 75° and ∠B = 110°. Find ∠C and ∠D.
Answer
Solution: Given: ∠A = 75°, ∠B = 110° Step 1: Use property of cyclic quadrilateral ∠A + ∠C = 180° (opposite angles) ∠B + ∠D = 180° (opposite angles) Step 2: Calculate ∠C 75° + ∠C = 180° ∠C = 180° - 7…
How do you construct a perpendicular to a line using the circle theorem?
Answer
Method using 'Angle in semicircle = 90°': Steps: 1. Draw a circle passing through the given point on the line 2. Ensure the circle intersects the line at another point 3. Draw the diameter through th…
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Sources & Official References
- Kerala Board of Public Examinations — keralapareekshabhavan.in
- National Education Policy 2020 — education.gov.in
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