A circle with its centre at O has two chords AB and BC such that point

Question

A circle with its centre at O has two chords AB and BC such that points A, B and C lie on the circumference of the circle. Are the chords AB and BC equal?

(1) Angle ABC is 90 degrees.

(2) Angle OAB is 50 degrees.

ReadyPlayerOne · Answer

Statement 1 is insufficient. 
Statement 2 Insufficient.

combining statement 1 and 2 is sufficient coz statement 1 tells us that the Line AC will be diameter and statement 2 tells us that angle a is 50 degree which bring us to the conclusion that the line ab and cb is not equal

KUDOS IF THIS WAS HELPFUL

Masterscorp · Answer

Can you please elaborate a bit more?

If we have a right angle on the line of the circle we know that AC is the diameter?

ReadyPlayerOne · Answer

Hi,

Its a property of circle that the triangle made from the diameter (with AC as diameter) then angle ABC (with point B on the circle) will be 90 degrees (vice versa is also true).

If I made the point clear then Kindly HIT KUDOS.

globaldesi · Answer

i think the answer should be B because anyways angle subtended by a diameter is 90 degrees and we are told other angle is 50
hence the third will be 40. Thus sides are not equal

adstudy · Answer

Yes true, angle subtended by a diameter is 90 degrees. But how do you know that AC is the diameter. No where in the question it is mentioned. I think you have subconsciously considered Statement 1 as a given condition.

A circle with its centre at O has two chords AB and BC such that point

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