MathDB
2008 JBMO Shortlist G7

Source: 2008 JBMO Shortlist G7

October 10, 2017
JBMOgeometry

Problem Statement

Let ABCABC be an isosceles triangle with AC=BCAC = BC. The point DD lies on the side ABAB such that the semicircle with diameter BDBD and center OO is tangent to the side ACAC in the point PP and intersects the side BCBC at the point QQ. The radius OPOP intersects the chord DQDQ at the point EE such that 5⋅PE=3⋅DE5 \cdot PE = 3 \cdot DE. Find the ratio ABBC\frac{AB}{BC} .
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