Example 1
If two intersecting chords of a circle make equal angles with the diameter passing through their point of intersection, prove that the chords are equal.
Given: Let AB & CD be two chords intersecting at E.
PQ is the diameter passing through E
AB & CD makes equal angles with diameter PQ
&., AEQ = DEQ
To prove: Chords are equal i.e., AB = CD
Construction: We draw OL AB & OM CD
Proof:
In OLE and OME,
OLE = OME
OEL = OEM
OE = OE
OLE OME
OL = OM
Here,
OL is the distance of chord AB from centre
& OM is the distance of chord CD from centre
Since OL = OM,
Chord AB & CD are equidistant from the centre
So, AB = CD
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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