SAT Math Multiple Choice Practice Question 548: Answer and Explanation
Note: Figure not drawn to scale.
In the figure above, lines k and l are tangent to the circle with center O at points A and C, respectively. If OB = 4, OA = AB, AB = BC, and ⊥ then OA =
Correct Answer: C
C Because lines k and l are tangent to the circle, they form right angles with the radii. Angles OAB, AOC, and OCB in quadrilateral OABC are all 90°, and all four angles must add to 360°, so the remaining angle must also be 90°, which makes OABC a rectangle. Because and are radii, they are equal, and you are told that is the same length as the other two sides. Thus, all four sides are equal. So OABC is actually a square. Draw in and you'll see that it bisects the square, forming two 45°-45°-90° triangles (see the reference information at the beginning of any SAT Math section). So OB = 4 = s. Solving for s gives you 2, which is the length of each side of the square.