Ex10.4, 3
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.
Given: Let AB & CD be the two equal
chords intersecting at point X.
⇒ AB = CD
To prove: OX makes equal angles with the chord
i.e. ∠ OXA = ∠ OXD
Proof: We draw OM ⊥ AB & ON ⊥ CD
In ΔOMX and ΔONX,
∠OMX = ∠ONX
OX = OX
OM = ON
∴ ΔOMX ≅ ΔONX
ΔOPX ≅ ΔOQX
∴ ∠OXM = ∠OXN
i.e., ∠ OXA = ∠ OXD
Hence proved

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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