ICSE Class 10Mathematics
⏱️ 14 min readCircles – Chords and Tangents
The angle subtended by an arc at the center is double the angle subtended at any point on the remaining circumference.; Opposite angles of a cyclic quadrilateral are supplementary (sum = 180°).
⚡ Essential Formula / LawCore Syllabus Rule
Tangent-Secant Theorem: PT² = PA × PB | Angle in alternate segment is equal
🎯 High-Yield Syllabus Checkpoints
- 1The angle subtended by an arc at the center is double the angle subtended at any point on the remaining circumference.
- 2Opposite angles of a cyclic quadrilateral are supplementary (sum = 180°).
- 3Tangents drawn from an external point to a circle are equal in length.
🚨 Examiner Traps & Common Mistakes
⚠️ Common Student Pitfall
Confusing cyclic quadrilateral properties with general four-sided quadrilaterals.
⚠️ Common Student Pitfall
In PT² = PA × PB, mistakenly measuring from the circle boundary rather than the external point P.
📚 Verified Technical Definitions
Cyclic Quadrilateral
A four-sided polygon whose four vertices all lie on the circumference of a single circle.
Alternate Segment Theorem
The angle between a tangent and a chord through the point of contact equals the angle in the alternate segment.
Spaced Repetition Protocol:
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