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Kite on the moon

A green kite BDHA shares the vertices D, H with a circle (DHJL). DA intersects the circle in the points D and J. The side HA, extended, meets the circle at L. Show that the angle between LJ and BD is the same as between AD and AH: is η = ε?

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Solution

Yes, η = ε.

Solution by Lewis Corner.

More solutions: https://x.com/Mirangu1/status/1883790932434428211

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