SAT Question of the Day Explained – October 1, 2015 – Math, Geometry, Triangles, Circles

Here’s today’s SAT question of the day, which is a math question about triangles and circles:

math geometry triangle circle

Hint: why do they tell us that ABC is equilateral?An equilateral triangle has 3 equal sides and 3 60 degree angles.  How does this help us?

Well, the circle has been divided into 3 equal parts, too, by this equilateral triangle.  So, each new arc is one third of the circle’s circumference – which includes arc AXB, which happens to be what the question asks us to find.

The circumference of the circle can be found with the formula C = Πd, or C = 2Πr.  Since our radius is just “r”, C does equal 2Πr for this circle.

But our arc is only 1/3 of 2Πr, so we end up with 2Πr/3.

Bonus question: what does inscribed mean??