SAT Practice Question | Geometry Math Problem

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The perpendicular line to the diameter bisects the chord, making the length of one side of the triangle, half of the chord's length. I had to cut some of the explanation off to fit this video into a short. Please leave any question you may have in the comment. Thanks for watching.

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No...that's incorrect..

Yes, the steps you've demonstrated are correct, yet, the final solution you've arrived at isn't correct. You see...,

Let's take the centre of AB to be O and that of CD to be O'

You've correctly identified that OD = r, OO' is the distance between AB and CD and O'D = ⅓AB = 2r/3

But that's just the length of O'D

Since ΔOO'D is right,

OO' = √(OD² – O'D²)
= √(r² – (2r/3)²)
= √(5r²/9) → r√5/3

∴ (D) is the required solution

ravipramod