Question

If AB and CD are two equal chords of a circle with centre O intersecting each other at

the point E, as shown in the given figure, find the relation between ∠ and ∠

with proper justification.​

Answer 1

Answer:AB and CD are two equal chords of a circle with centre O intersecting each other at the point E.

In ∆EMO and ∆ENO

i) ∠EMO = ∠ENO = 90°

ii) EO is common.

iii) MO = NO (Equal chords of a circle are equidistant from the center.)

∴∆EMO ≅ ∆ENO (RHS)

∴∠MEO = ∠NEO (cpct)

∴∠BEQ = ∠CEQ