Ex 9.2, 2
If two equal chords of a circle intersect within the circle, prove that the segments of one chord are equal to corresponding segments of the other chord.
Given: Let AB & CD be the two equal chords
intersecting at point X.
⇒ AB = CD
To prove: Corresponding segments are equal, i.e.,
AX = DX
and
BX = CX
Proof: We draw OM ⊥ AB & ON ⊥ CD
So, AM = BM = 1/2 AB
& DN = CN = 1/2 CD
As AB = CD,
⇒ 1/2 AB = 1/2 CD
∴ AM = DN
& MB = CN
In ΔOMX and ΔONX,
∠OMX = ∠ONX
OX = OX
OM = ON
∴ ΔOMX ≅ ΔONX
∴ MX = NX
Adding (1) & (3)
AM + MX = DN + NX
AX = DX
Therefore,
AX = DX & BX = CX
Hence proved

Made by

Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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