Find the value of $x$ in the given figure if $∠ A O B = 70^{\circ}$ and $A B = C D .$

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Solution

From the given figure, AB and CD are chords.
Given: $A B = C D ∠ A O B = 70 °$

The angle subtended by the chord AB is $∠ A O B,$ and the angle subtended by the chord CD is $∠ C O D = x .$

We know that, equal chords subtend equal angles at the centre.
$\Rightarrow ∠ A O B = ∠ C O D = x$
Thus, $x = 70^{\circ} .$

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