# 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.

**Solution:**

Let AB and CD be the two equal chords. AB = CD.

Let the chords intersect at point E. Join OE.

Draw perpendiculars from the center O to the chords. The Perpendicular bisects the chord AB at M and CD at N.

To prove: ∠OEN = ∠OEM.

In ∆OME and ∆ONE,

∠M = ∠N = 90°

OE = OE

OM = ON (Equal chords are equidistant from the center.)

By RHS criteria, ∆OME and ∆ONE are congruent. So, by CPCT, ∠OEN = ∠OEM

Hence proved that the line joining the point of intersection of two equal chords to the center makes equal angles with the chords.

**Video Solution:**

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

### Maths NCERT Solutions Class 9 - Chapter 10 Exercise 10.4 Question 3:

**Summary:**

If two equal chords of a circle intersect within the circle, then the line joining the point of intersection to the center makes equal angles with the chords.