Geometry Problem. Post your solution in the comment box below.

Level: Mathematics Education, High School, Honors Geometry, College.

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## Thursday, August 18, 2016

### Geometry Problem 1248: Triangle, Circumcircle, Circle, Diameter, Orthocenter, Altitude, Parallel Lines

Labels:
altitude,
circle,
circumcircle,
diameter,
orthocenter,
parallel,
perpendicular,
triangle

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Connect KC,

ReplyDeleteQuadrilateral AEDC is cyclic => ∠ (BED)= ∠ (ACB) .. ( both angles supplement to ∠ (AED))

we have ∠ (BAC)= ∠ (BKC) => ∠ (ABF)= ∠ (KBC)

so triangle BEG similar to BCM and triangles BEH similar to BCK …( case AA)

and we have BG/BM=BE/BC=BH/BK

so BG/BH=BM/BK

and GM//HK