In the figure below, ABC is equilateral. P is a point inside ABC such that BPC is a right isosceles triangle. What is ABP in degrees?

https://latex.artofproblemsolving.com/7/1/d/71daedfa74cc903aeb2620c72d5d2ec34dbfcfd8.png

Saketh Sep 24, 2019

#1**-1 **

In the figure above, triangle ABC is equilateral, and point P is equidistant from vertices A, B, and C. If triangle ABC is rotated clockwise about point P, what is the minimum number of degrees the triangle must be rotated so that point B will be in the position where point A is now?

(A) 60

(B) 120

(C) 180

(D) 240

(E) 270

Look at the diagram below:

Each of the three red central angles is 120° (360°/3 = 120°). Thus in order point B to be in the position where point A is, the triangle should be rotated clockwise by 120° + 120° = 240°.

Answer: D.

killersteve27 Sep 24, 2019