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

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

Click the figure below to view more details of problem 1231.

## Tuesday, July 5, 2016

### Geometry Problem 1231: Triangle, Orthocenter, Incenter, Circumcenter, Angle Bisector, Center, Circle

Labels:
angle bisector,
center,
circle,
circumcenter,
incenter,
orthocenter,
triangle

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https://goo.gl/photos/eZPPUPkAJ3njjb2E7

ReplyDeleteDraw OD ⊥ to AC ( D is on the circle O)

D is the midpoint of arc AC

since BI is the angle bisector of ∠(ABC) => B, I, D are collinear

Triangle BOD is isoceles => ∠(OBI)=∠(ODI)

but ∠(ODI)=∠(HBI) => ∠(HBI)=∠(OBI) => BI is the angle bisector of ∠( HBO)

see correct link to this problem below:

Deletehttps://goo.gl/photos/NtEqqUcJsf3GfQgm6

Peter Tran

PrĂ¸blem 1231

ReplyDelete< ABI = < CBI ......(1)

< ABH = < CBO = 90-A ....(2)

(1) - (2) gives the required result

Sumith Peiris

Moratuwa

Sri Lanka