Free help with homework

Why join Brainly?

  • ask questions about your assignment
  • get answers with explanations
  • find similar questions

If two equal chords of a circle intersect within the circle , prove that the segments of one chord are equal to the corresponding segments of the other



Given AB and CD are chords of a circle with centre O. AB and CD intersect at P and AB = CD.
To prove : AP = PD and PB = CP.
Construction: Draw OM perpendicular to AB and ON perpendicular CD. Join OP.

AM = MB = 1/2AB (Perpendicular bisecting the chord)
CN = ND = 1/2CD (Perpendicular bisecting the chord)
AM = ND and MB = CN (As AB = CD)
In triangle OMP and ONP, we have,
OM = MN (Equal chords are equidistant from the centre)
<OMP = <ONP (90⁰)
OP is common. Thus triangle OMP and ONP are congruent (RHS).
MP = PN (cpct)
So, AM + MP = ND + PN
or, AP = PD (i)

As MB = CN and MP = PN,
MB - MP = CN - PN 
= PB = CP (ii)

Hope that helps !!
0 0 0
The Brain
  • The Brain
  • Helper
Not sure about the answer?
Learn more with Brainly!
Having trouble with your homework?
Get free help!
  • 80% of questions are answered in under 10 minutes
  • Answers come with explanations, so that you can learn
  • Answer quality is ensured by our experts