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/sci/ - Science & Math

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4729781 No.4729781[STICKY]  [Reply] [Original]

A convex hexagon <span class="math">ABCDEF[/spoiler] is inscribed in a circle such that <span class="math">AB = CD = EF[/spoiler] and diagonals <span class="math">AD[/spoiler], <span class="math">BE[/spoiler], and <span class="math">CF[/spoiler] are concurrent. Let <span class="math">P[/spoiler] be the intersection of <span class="math">AD[/spoiler] and <span class="math">CE[/spoiler]. Prove that <span class="math">CP/PE = (AC/CE)^2[/spoiler].

>> No.4730067
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4730067

I got this.

>> No.4730073

drawing pls

>> No.4730266
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4730266

according to my calculations....
the best time for cp is during pe

>> No.4730380
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4730380

>>4730266
I couldnt agree more.

>> No.4730655 [DELETED] 

Do you guys actually can solve this?

>> No.4730956
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4730956

>>4730266

>> No.4731879

>>4730266
Good one

>> No.4732063
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4732063

>>4730266

Will this work?

>> No.4732694

aren't CE and AC the same length?

so all you have to prove is that PE=CP right?

>> No.4732895

CP/PE=(AC/CE)^2