Circles
ICSE · Class 10 · Mathematics
Flashcards for Circles — ICSE Class 10 Mathematics. Quick Q&A cards covering key concepts, definitions, and formulas.
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Get startedA circle has centre O and radius 7 cm. Write the formula for a circle and state why the radius is always positive.
Answer
Formula idea: A circle is the set of all points at a constant distance from a fixed point. Step 1: The fixed point is called the centre. Step 2: The constant distance is called the radius. Step 3: The…
Find the degree measure of arc PQ if the angle subtended by arc PQ at point R on the circle is 35°.
Answer
Use the degree measure theorem. Step 1: Degree measure of arc PQ = 2 × angle subtended at the point on the circle. Step 2: Arc PQ = 2 × 35°. Step 3: Arc PQ = 70°. Answer: 70°…
Why are angles in the same segment of a circle equal? Give a quick reasoning from the angle theorem.
Answer
Step 1: Two angles in the same segment subtend the same arc. Step 2: Each angle at the circle equals half the angle subtended by the same arc at the centre. Step 3: Since both depend on the same centr…
A chord PQ is a diameter. Find the angle subtended by PQ at any point R on the remaining part of the circle.
Answer
Use the angle in a semicircle theorem. Step 1: A diameter subtends a straight angle at the centre, so ∠POQ = 180°. Step 2: Angle at the circle is half the angle at the centre. Step 3: ∠PRQ = 180° ÷ 2 …
A point R on a circle sees chord PQ under 48°. What is the angle seen by another point S in the same segment on the same side of PQ?
Answer
Step 1: Angles in the same segment of a circle are equal. Step 2: So ∠PRQ = ∠PSQ. Step 3: Given ∠PRQ = 48°. Answer: ∠PSQ = 48°…
Show that if an angle subtended by an arc is 90° at a point on the circle, then the arc is a semicircle.
Answer
Step 1: Let the arc subtend angle 90° at a point on the circle. Step 2: Angle at the centre = 2 × angle at the circle. Step 3: Central angle = 2 × 90° = 180°. Step 4: A 180° central angle means the en…
Three points P, Q, and R lie on a circle. Point S is on the same side of line PQ and ∠PRQ = ∠PSQ. What can be said about P, Q, R, S?
Answer
Step 1: A line segment subtending equal angles at two points on the same side implies the four points are concyclic. Step 2: Since ∠PRQ = ∠PSQ, points P, Q, R, S lie on one circle. Answer: The four po…
A cyclic quadrilateral ABCD has ∠A = 72°. Find ∠C.
Answer
Use opposite angles of a cyclic quadrilateral. Step 1: ∠A + ∠C = 180°. Step 2: 72° + ∠C = 180°. Step 3: ∠C = 180° - 72° = 108°. Answer: 108°…
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