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MathNet 2008-part-02 — 165 problems (EN–VI) Question 55

Math Olympiad Vault · MathNet 2008-part-02 — 165 problems (EN–VI)

Question 55

In an isosceles trapezoid $ABCD$ with larger base $AB$, the diagonals are divided by their intersection point $O$ into parts proportional to the numbers 1 and 3. Knowing that the area of triangle $BOC$ is 15, what is the area of the whole trapezoid?

Question illustration

(A) 60
(B) 75
(C) 80
(D) 90
(E) 105.