# ACT Math: A Challenging Circle Problem

Here’s another challenging problem for you, this one involving circles. You’ll need to use concepts you’ve learned in both Algebra and Geometry to get this one right. Good luck!

In the circle below with center at Point O, the length of chord AB is 30 units. The radius in the diagram is perpendicular to the chord AB, which cuts the radius into two pieces with lengths of x units and x + 1 units as labeled in the diagram. What is the length, in units, of the radius of the circle?

A.  13
B.  15
C.  17
D.  18
E.  20

# A Challenging Algebra & Geometry Problem

Are you up for another challenging ACT Math problem? This one will require you to use concepts you’ve learned in both Algebra and Geometry.

The equation of the parabola in the figure below is f(x) = -12/25 x2 + 12. Point A is a vertex of the triangle and the y-intercept of the parabola. Points B and C are also vertices of the triangle and the x-intercepts of the parabola. What is the perimeter of triangle ABC ?

A.  24
B.  28
C.  30
D.  32
E.  36

# SAT Math: Functions That Intersect Geometric Figures

This post addresses another of the types of problems that appear near the end of an SAT Math section among the harder questions. This type of problem requires you to integrate what you know about functions with your knowledge of geometry. Most of these problems are multi-step and require you to think ahead about what you need to know in order to solve the problem and how you can figure those things out.

Let’s consider a problem:

Triangle ABC is isosceles and has a perimeter of 32.  The vertices of its base are (-6,0) and (6, 0). The parabola has its vertex at (0, -2) and it intersects the triangle at the midpoints of segments AB and AC. If the parabola has an equation in the form f(x) = ax² + k, what is the value of a?

(A)  -1/3
(B)  1/3
(C)  2/3
(D)  3/4
(E)  4/3