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computational, <C=2A, D \in AC , <ABD = <DBC, AB = 10, CD = 3,

Source: 2020 Portugal p2

October 11, 2020
geometryequal segmentsequal angles

Problem Statement

In a triangle [ABC][ABC], ∠C=2∠A\angle C = 2\angle A. A point DD is marked on the side [AC][AC] such that ∠ABD=∠DBC\angle ABD = \angle DBC. Knowing that AB=10AB = 10 and CD=3CD = 3, what is the length of the side [BC][BC]?
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