Circles
ICSE · Class 10 · Mathematics
Flashcards for Circles — ICSE Class 10 Mathematics. Quick Q&A cards covering key concepts, definitions, and formulas.
What 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
+14 more flashcards available
Practice AllGet detailed flashcards for Circles
Super Tutor gives you interactive content for every chapter of ICSE Class 10 Mathematics — summaries, quizzes, flashcards, and more.
Try Super Tutor — It's FreeFrequently Asked Questions
What are the important topics in Circles for ICSE Class 10 Mathematics?
Circles covers several key topics that are frequently asked in ICSE Class 10 board exams. Focus on the core concepts listed on this page and practise related questions to build confidence.
How to score full marks in Circles — ICSE Class 10 Mathematics?
Start by understanding all key concepts. Practise previous year questions from this chapter. Revise formulas and definitions regularly. Use flashcards for quick revision before the exam.
How many flashcards are available for Circles?
There are 22 flashcards for Circles covering key definitions, formulas, and concepts. Use them daily for 10–15 minutes for best results.
Sources & Official References
Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.
More Resources for Circles
Important Questions
Practice with board exam-style questions
Syllabus
What topics to cover
Revision Notes
Key points for last-minute revision
Study Plan
Step-by-step plan to ace this chapter
Formula Sheet
All formulas in one place
Chapter Summary
Understand the chapter at a glance
Practice Quiz
Test yourself with a quick quiz
Concept Maps
See how topics connect visually