Question

Ab and bc are two chords of a circle and they are equally inclined to the diameter drawn through b.prove that the chords are equal.

Answer 1

Answer:

Let AB and AC be two chords and AOD be a diameter such that.

∠BAO = ∠CAO

Draw OL ⊥ AB and OM ⊥ AC

Now prove, ΔOLA = ΔOMA

Then OL = OM ⇒ AB = CD

(Chords which are equidistant from the centre are equal )

Hence proved.

Answer 2

Explanation:

To prove : AB = BC

Construsct : OM perpendicular to AB and

ON perpendicular to BC

Therefore, In ∆ OMB and ONB

Angle 1 = angle 2

angle OMB = angle ONB (90°)

OB = OB (common side)

∆OMB congruent to ∆ONB (by AAS)

Therefore, MB = NB ( by CPCT )

2MB = 2NB ( multiplying 2 on both

sides)

So, AB = BC

Hence proved