Problem:
Triangle ABC is a right triangle with ∠ACB as its right angle, m∠ABC=60∘, and AB=10. Let P be randomly chosen inside △ABC, and extend BP to meet AC at D. What is the probability that BD>52 ?
Answer Choices:
A. 22−2
B. 31
C. 33−3
D. 21
E. 55−5 Solution:
Since AB is 10 , we have BC=5 and AC=53. Choose E on AC so that CE=5. Then BE=52. For BD to be greater than 52,P has to be inside △ABE. The probability that P is inside △ABE is
Area of △ABC Area of △ABE=21CA⋅BC21EA⋅BC=ACEA=5353−5=33−1=33−3.
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