Example no - 2 solution Fig. 10.23
them. This verifies the converse of the Theorem 10.6 which is stated as follows..
r heorem 10.7 Chords equidistant from the centre of a circle are equal in
We now take an example to illustrate the use of thulbove results:
Example 2 : If two intersecting chords of a circle make equal angles with the diametet
passing through their point of intersection, prove that the chords are equal.
Solution : Given that AB and CD are two chords of
a circle, with centre O intersecting at a point E. PQ
is a diameter through E, such that Z AEQ = Z DEQ
(see Fig. 10.24). You have to prove that AB = CD.
raw perpendiculars OL and 0M on chords AB and
D, respectively.. Now
LOE= 1800 900 -Z LEO = 900 -Z LEO
n trinncvløh
c
