Advertisement Remove all ads

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. - Mathematics

Advertisement Remove all ads
Advertisement Remove all ads
Advertisement Remove all ads

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.

Advertisement Remove all ads

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 ΔOVT and ΔOUT,

OV = OU (Equal chords of a circle are equidistant from the centre)

∠OVT = ∠OUT (Each 90°)

OT = OT (Common)

∴ ΔOVT ≅ ΔOUT (RHS congruence rule)

∴ ∠OTV = ∠OTU (By CPCT)

Therefore, it is proved that the line joining the point of intersection to the centre makes equal angles with the chords.

Concept: Equal Chords and Their Distances from the Centre
  Is there an error in this question or solution?

APPEARS IN

NCERT Class 9 Maths
Chapter 10 Circles
Exercise 10.4 | Q 3 | Page 179

Video TutorialsVIEW ALL [1]

Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×