Question -
Answer -
From the question weknow the following:
(i) AB and CD are 2chords which are intersecting at point E.
(ii) PQ is thediameter of the circle.
(iii) AB = CD.
Now, we will have toprove that BEQ = CEQ
For this, thefollowing construction has to be done:
Construction:
Draw two perpendiculars aredrawn as OM ⊥ AB and ON ⊥ D. Now, join OE. Theconstructed diagram will look as follows:Now, consider thetriangles ΔOEM and ΔOEN.
Here,
(i) OM = ON [Since theequal chords are always equidistant from the centre]
(ii) OE = OE [It isthe common side]
(iii) OME = ONE [Theseare the perpendiculars]
So, by RHS congruencycriterion, ΔOEM ΔOEN.
Hence, by CPCT rule,MEO = NEO
∴ BEQ = CEQ (Hence proved).