Ridiculous Circle Geometry Question... (1 Viewer)

[hyparzero]

I am having trouble proving the following question:

(There were no diagrams for this question!)

1. Let O be the circumcenter of DABC. Suppose AB > AC > BC. Let D be a point on the minor arc BC. Let E and F be points on AD such that AB is perpendicular to OE and AC is perpendicular to OF. Let P be the intersection of BE and CF.

If PB = PC+PO, then prove that Angle BAC = 30°.


I feel the question was too hard to be regarded as a Extension 1 Maths question, so I posted here in the Extension 2 Maths Forum, but please move it if i have made a mistake.

Help would be appreciated. Thanks!

 

[Mountain.Dew]

I am having trouble proving the following question:

Let E and F be points on AD such that AB ^ OE and AC ^ OF. Let P be the intersection of BE and CF.

I feel the question was too hard to be regarded as a Extension 1 Maths question, so I posted here in the Extension 2 Maths Forum, but please move it if i have made a mistake.

Help would be appreciated. Thanks!

what does AB ^ OE and AC ^ OF mean? AB is parallel to OE? or AB is perpedicular to OE? please be more specific...

this seems quite a challenging question.

 

[hyparzero]

yes, sorry, i've edited the question, now it looks right...

thanks

 

[Riviet]

Had a look at this question, very challenging from what I can see, especially with the inequality of the 3 sides and the sum of two sides equalling another. Just remember you're going to have to use those conditions to assist you with the proof.
Here's my last cent: Since OE | AB and passes through O when extended to the circumference of the circle, OE bisects AB. Similar thing with OF and AC. Hope that helps. =]