Question 3
If two equal chords of a circle intersect within the circle, prove that the line joining the point of intersection to the centre makes equal angles with the chords.

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Solution

Let PQ and RS are two equal chords of a given circle and they are intersecting each other at point T.
Draw perpendiculars OV and OU on these chords.
In $Δ O V T$ and $Δ O U T$
OV = OU (Equal chords of a circle are equidistant from the centre)
$∠ O V T = ∠ O U T (E a c h 90^{\circ})$
OT = OT (Common)
$∴ Δ O V T ≅ Δ O U T$ (RHS congruence rule)
$∴ ∠ O T V = ∠ O T U (B y C P C T)$
Therefore, it is proved that the line joining the point of intersection to the centre makes equal angles with the chords.

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Question 3 If two equal chords of a circle intersect within the circle, prove that the line joining the point of intersection to the centre makes equal angles with the chords.

Question 3
If two equal chords of a circle intersect within the circle, prove that the line joining the point of intersection to the centre makes equal angles with the chords.