Question

L and M are midpoints of two equal chords AB and CD, O is the centre of the circle, prove that angle OLM = angle OML and angle ALM = angle CML

Answer 1

[FIGURE IS IN THE ATTACHMENT]
GIVEN:
AB and CD are two equal chords of a circle with Centre O. L is the midpoint of AB and M is the midpoint of CD.
To Prove:(i) ∠OLM = ∠OML
(ii) ∠ALM = ∠CML
PROOF:
L is the midpoint of chord AB of circle with Centre O.
OL ⟂AB & OM ⟂CD
[The line joining the centre of the midpoint of a chord is perpendicular to the chord]
Chord AB = chord CD (given)
OL = OM (equal chords are equidistant from the centre)
In ∆OLM,
OL = OM (proved above)
∠OLM = ∠OML (angle opposite to equal sides of a triangle are equal)..............(1)
∠OLA = ∠OMC. (Each 90°)..........(2)
On adding eqs 1 &2
∠OLM + ∠OLA = ∠OML + ∠OMC
∠ALM = ∠CML

HOPE THIS WILL HELP YOU….

Answer 2

Answer:

this answer is for bachelor‍‍