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 startedWhat is a circle? Define it mathematically.
Answer
A circle is the locus of a point which moves in a plane so that its distance from a fixed point in that plane always remains constant. The fixed point is called the centre and the constant distance is…
State the theorem about the angle subtended by an arc at the centre and at any point on the circle.
Answer
The degree measure of an arc of a circle is twice the angle subtended by it at any point in the alternate segment of the circle with respect to the arc. In formula: ∠POQ = 2∠PRQ, where O is centre, PQ…
What can you say about angles in the same segment of a circle?
Answer
Angles in the same segment of a circle are equal. This means if two angles are subtended by the same arc and the vertices of both angles lie in the same segment of the circle, then these angles are eq…
What is the measure of an angle in a semicircle?
Answer
An angle in a semicircle is a right angle (90°). This is because the angle subtended by a diameter at any point on the circle is 90°. If PQ is a diameter and R is any point on the circle, then ∠PRQ = …
State the property of opposite angles in a cyclic quadrilateral.
Answer
The sum of either pair of opposite angles of a cyclic quadrilateral is 180°. If ABCD is a cyclic quadrilateral, then ∠A + ∠C = 180° and ∠B + ∠D = 180°. This means opposite angles are supplementary.
What is the relationship between an exterior angle of a cyclic quadrilateral and the opposite interior angle?
Answer
The exterior angle of a cyclic quadrilateral is equal to the opposite interior angle. If ABCD is cyclic and AB is extended to E, then ∠CBE = ∠ADC. This property helps identify cyclic quadrilaterals.
How can you prove that four points are concyclic?
Answer
Four points are concyclic if: (1) A line segment joining two points subtends equal angles at two other points lying on the same side, OR (2) The sum of opposite angles of the quadrilateral formed is 1…
What is a tangent to a circle?
Answer
A tangent to a circle is a line that touches the circle at exactly one point. This point is called the point of contact or point of tangency. The tangent lies entirely outside the circle except at the…
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