Circle — Chapter Summary
Maharashtra Board · Class 10 · Mathematics
Summary of Circle for Maharashtra Board Class 10 Mathematics. Part of the Maharashtra Board Class 10 Mathematics syllabus.
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Overview
Count the main ideas: circles through points, tangents and secants, touching circles, arcs and their measures, congruent arcs, inscribed angles, cyclic quadrilaterals, tangent–chord angles, and products of segments. The whole chapter links line–circle relationships with angle rules and length rules,
Key Concepts
One point allows infinitely many circles
One point allows infinitely many circles. Two distinct points also allow infinitely many circles, and their centres lie on the perpendicular bisector
A tangent touches a circle at
A tangent touches a circle at exactly one point, called the point of contact. A secant cuts a circle at two points. A line with no common point with a
A tangent at any point
A tangent at any point of a circle is perpendicular to the radius at the point of contact. Also, a line perpendicular to a radius at its point on the
Tangent segments drawn from an external
Tangent segments drawn from an external point to a circle are congruent. If two tangents are drawn from the same outside point, their lengths are equa
If two circles touch
If two circles touch, their point of contact lies on the line joining their centres. For externally touching circles, the distance between centres equ
Learning Objectives
- Identify a tangent, secant, chord, arc, central angle, inscribed angle, and cyclic quadrilateral.
- Use tangent theorems to find unknown angles and prove perpendicularity.
- Apply properties of touching circles, including the position of the point of contact and the distance between centres.
- Compare minor arcs, major arcs, and semicircular arcs using their measures.
- Use the inscribed angle theorem and its corollaries in angle problems.
Frequently Asked Questions
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Sources & Official References
Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.
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