Question

In the given figure if AB is the diameter and EC = ED prove that angle COF = angle CEF

Answer 1

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Solution:

In ∆ POF and ∆ PEC,

∠OFP = ∠PCE ( Inscribed angles subtended by the same arc are equal )

∠FPO = ∠CPE ( vertically opposite )

∠POF = ∠PCF ( alternate angles )

Hence, By AAA property,

∆ POF ≅ ∆ PEC

∴ ∠ COF = ∠ CEF

( CORRESPONDING ANGLES OF CONGRUENT TRIANGLES )

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