If - - 40- and - - - then find the measure of -

Construction: Draw lines OB, OC, and OD. In nbsp;ΔAOB, OA = OB (Radii of the same circle) Thus, ∠OAB = ∠OBA = 40°. (Angles opposite to equal sides of a triang ...

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Byju's Answer

Standard X

Mathematics

Division of a Line Segment

If ∠𝑂𝐴𝐵 = ...

Question

If ∠𝑂𝐴𝐵 = 40° and 𝐴𝐵 = 𝐶𝐷, then find the measure of ∠𝐶𝑂𝐷.

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Solution

Construction: Draw lines OB, OC, and OD.
In ΔAOB,
OA = OB (Radii of the same circle)
Thus, ∠OAB = ∠OBA = 40°.
(Angles opposite to equal sides of a triangle).
So, by angle sum property, ∠AOB = 100°.

Since the chords AB and CD are equal in length, the angles subtended by them at the centre will be equal.

Hence, ∠AOB = ∠COD = 100°.

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