Geometry Problem 1485. Post your solution in the comment box below.

Level: Mathematics Education, K-12 School, Honors Geometry, College.

Details: Click on the figure below.

## Wednesday, November 25, 2020

### Geometry Problem 1485: Triangle, Orthocenter, Altitude, Circle, Diameter, Tangent, Measurement

Labels:
altitude,
circle,
diameter,
geometry problem,
measurement,
orthocenter,
tangent,
triangle

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https://photos.app.goo.gl/v7KgdZECAesRBJjr9

ReplyDeleteDraw altitude BD of triangle ABC ( see sketch)

We have B, H, D are collinear ( H is the orthocenter)

Quadrilateral ADEB is cyclic so HE.HA=HB.HD= 140

In cycle BTDC we have HT.HF=HB.HD=140

So HF= 140/HT=8.5

minor correction of the last line:

DeleteSo HF= 140/HT=8.75

Draw altitude BP

ReplyDeleteWe have BH . HP = 140

=> TH . HF = 140 => HF = 8.75

https://photos.app.goo.gl/7F46Z7YkTbVG5kkk9

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