SS2: MATHEMATICS - 3RD TERM
Graphical Solution of Linear & Quadratic Equations | Week 12 Topics|1 Quiz
Circle Geometry I | Week 25 Topics
Circle Geometry II | Week 34 Topics|1 Quiz
Construction of Quadrilaterals | Week 42 Topics
Linear Inequalities | Week 53 Topics|1 Quiz
Trigonometry I | Week 64 Topics
Trigonometry II | Week 72 Topics|1 Quiz
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
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
In the diagram below find the value of the chord DC.
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