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MathNet 2023-part-01 — 191 problems (EN–VI) Question 7

Math Olympiad Vault · MathNet 2023-part-01 — 191 problems (EN–VI)

Question 7

Let $ABCD$ be a convex quadrilateral that satisfies the following conditions:
$$
\angle BAC = 2\angle BCA, \quad \angle BCA + \angle CAD = 90^\circ \quad \text{and} \quad BC = BD.
$$
Find $\angle ADB$.