# SAT Math Multiple Choice Practice Question 548: Answer and Explanation

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**Question: 548**

**5.**

__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* =

A.

B. 2

C. 2

D. 4

E. 4

**Correct Answer:** C

**Explanation:**

**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.