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MathNet 2016-part-05 — 184 problems (EN–VI) Question 74

Math Olympiad Vault · MathNet 2016-part-05 — 184 problems (EN–VI)

Question 74

The lines containing the chords $AC$ and $BD$ of a circle with radius $1$ intersect at an angle of $45^\circ$. The length of the chord $AB$ equals $1$ (see figure).
Question illustration
What is the size of the angle $\angle CBD$?

(A) $45^\circ$
(B) $60^\circ$
(C) $65^\circ$
(D) $75^\circ$
(E) $85^\circ$