Question

Please Solve this Question and give answer Quickly ​

Answer 1

Step-by-step explanation:

Given:- A Circle with centre O, AB and CD are chords of the circle, AB = CD

To Prove:-

a) OL = OM

b)∠OLM = ∠OML

c) ∠ALM = ∠CML

d) arc.AB = arc.CD

Proof:-

a)

AB and CD are chords and AB = CD

Thus, we know that, equal chords are equidistant from the centre of a circle.

∴ OL = OM [By theorem]

b)

In ΔOLM

OL = OM

∴ ∠OLM = ∠OML [Angles opposite to equal sides are equal] OR [Properties of Isosceles Triangle]

c)

Now,

L and M are midpoint of AB and CD respectively,

Thus,

OL ⊥ AB and OM ⊥ CD

[If a Line drawn from the centre of the circle bisects a chord, then that line is perpendicular to the chord]

Thus,

∠ALO = 90° [OL ⊥ AB]

∠CMO = 90° [OM ⊥ CD]

∴ ∠ALO = ∠CMO

Now,

∠OLM = ∠OML

90° - ∠OLM = 90° - ∠OML

From above we get,

∠ALO - ∠OLM = ∠CMO - ∠OML

∴ ∠ALM = ∠CML

d)

Now, we know that,

Arc subtended by equal chords are equal.

∴ arc.AB = arc.CD [By theorem]

Hope it helped and believing you understood it........All the best