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.
☛ Check: NCERT Solutions for Class 9 Maths Chapter 10
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.
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