# Quick Geometry!

**Geometry**Level 2

Consider an equilateral triangle ABC of side r. Reflect A about BC to form a point D. Let E be the midpoint of BD and F be the reflection of E about DC. Let there be a point P such that triangle ABF is congruent to triangle ACP. Consider the triangle FPA. Let I be the incentre, O be the orthocentre of FPA. Let the circumcentre of AIO be X. Draw a circle of radius r passing through X, and let Y be a point such that XY is the diameter. In the circle passing through X and Y, let M and N be points such that B is tangent to the circle at points M and N respectively. Using only elementary geometry, find angle ABD in degrees.

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