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Question
In AB and BC are two chords of a circle with centre O such that, ∠ABO = ∠ACO, prove that: AB = AC.
Theorem
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Solution
Given:
AB and BC are two chords of a circle with centre O such that ∠ABO = ∠ACO.
Join AO, BO, and CO.
In triangles ABO and ACO:
AO is common.
∠ABO = ∠ACO ... [given]
OB = OC
By the RHS (Right angle-Hypotenuse-Side) congruence criterion, ΔABO ≅ ΔACO.
Therefore, by CPCT (Corresponding Parts of Congruent Triangles), AB = AC.
Hence proved: AB equals AC.
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