MATH SAT QUESTION?

We know OA = OB = AB = r
So we have an equilateral triangle

And the distance between AB and O is the height of the perpendicular from O to AB,
This video will give the answer https://www.youtube.com/watch?v=ybhBkHJQoMU

1.
Let M be the mid-point of AB.
Then, AM = AB/2 = r/2 cm

Join OM. OM ⊥AB
Then, ΔAOM is a right-angled triangle with ∠AMO = 90°

In ΔAOM :
AM² + OM² = OA² …. (Pythagorean theorem)
(r/2 cm)² + OM² = (r cm)²
(r²/4 cm²) + OM² = (r² cm²)
OM² = (3/4)r² cm²
OM = (√3/2)r cm

The answer: C. (√3/2)r

OAB is a Equilateral triangle => angle A = 60°
Let C be the point in the middle of AB and we are going to find OD.
Angle OAC = 60/2° = 30°, and OCA = 90°

OAD is a triangle with sides: r, r/2 and OD
OD = r * cos 30°
OD = √3/2 r

If you draw a line from B to O, you have an equilateral triangle. The perpendicular segment from AB to O forms a 30-60-90 right triangle.