SS2: MATHEMATICS - 2ND TERM
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Linear Equations & Formulae5 Topics|1 Quiz
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Simultaneous Equations I2 Topics
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Simultaneous Equations II2 Topics|1 Quiz
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Graphical Solution of Linear & Quadratic Equations2 Topics|1 Quiz
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Linear Inequalities3 Topics|1 Quiz
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Algebraic Fractions5 Topics|1 Quiz
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Circle Geometry I | Week 25 Topics
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Circle Geometry II | Week 34 Topics|1 Quiz
Angles Suspended by Chords in a Circle
Topic Content:
- Angles Suspended by Chords in a Circle
Theorem: Equal chords of a circle subtend equal angles at the centre of the circle.
In a circle, if we draw two chords of equal lengths then the angles subtended by both the chords at the centre of the circle are equal.
Given: a circle with centre O with two chords of equal length, PQ and RS.

To prove: PQ and RS subtend equal angles at the centre.
i.e ∠POQ = ∠ROS
Proof:
PQ = RS (equal chords given)
OP = OR (Radii of the same circle)
OQ = OS (Radii of the same circle)
Triangles POQ and ROS are congruent: △POQ ≅ △ROS (SSS)
∴ ∠POQ = ∠ROS
Example 7.2.1:
In the diagram below find the value of the chord DC.

Solution:
Chords AB and DC form equal angles at the centre (60°)
We know that If the angles subtended by the chords of a circle at the centre are equal, then the chords are equal.
Thus, the length of AB and DC are equal.
From the diagram AB = 7
∴ DC = 7