geo7 - Problems in Geometry (7) 1. Let ϕ be an ellipse...

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Unformatted text preview: Problems in Geometry (7) 1. Let ϕ be an ellipse with foci F,F . If the tangent lines at A,B ∈ ϕ intersect in P , prove that PF ⊥ AB iff F ∈ AB . 1 2. Let ϕ be an ellipse with foci F,F . Let t,t be the tangents to ϕ which intersect in P . If H,H are respectively the feet of the perpendiculars from F on t,t , prove that PF is perpendicular to HH . 2 3. Let ϕ be an ellipse of foci F,F . Let ϕ ∩ FF = { A,A } . Let ‘,‘ be the tangents to ϕ. at A,A . For any tangent t to ϕ at M ∈ ϕ let t ∩ ‘ = { P } ,t ∩ ‘ = { P } . (A) Prove that < ( FP,FP ) = < ( F P,F P ) = π/ 2 3 . (B) Prove that FP,F P intersect on the normal to ϕ at M. 4 4. Let ϕ be an ellipse of foci F,F . Consider X ∈ ϕ. Let Q,Q be the points in which the normal of ϕ at X intersects the perpendiculars to XF,XF erected at F,F respectively. Prove that, the perpendicular bisector of [ FF ] bisects [ Q,Q ] ....
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This note was uploaded on 11/14/2011 for the course MATH 373 taught by Professor Cemtezer during the Spring '11 term at Middle East Technical University.

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geo7 - Problems in Geometry (7) 1. Let ϕ be an ellipse...

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