Question

A chord and the diameter through one of its ends are drawn in a circle. A chord of the same inclination is drawn on the other side of the diameter.

Answer 1

Given : A chord and the diameter through one of its ends are drawn in a circle .

A chord of the same inclination is drawn on the other side of the diameter.

To Find : prove that the chords are of the same length ​

Solution:

Let call chords as AB  & AC

and join BO  & CO

where O is center of the circle

∠BAO = ∠CAO  given

OA = OB  = Radius

=> ∠ABO = ∠BAO

OA = OC  = Radius

=> ∠CAO = ACO

=> ΔABO ≈ ΔACO  ( AA similarity criteria)

=> AB/AC = AO/AO  = BO/CO

=> AB/AC = 1

=> AB = AC

QED

Hence proved

A chord of the same inclination drawn on the other side of the diameter is of same length

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