Proposed Problem

Click the figure below to see the complete problem 373 about Square, Inscribed Circle, Diagonal, Perpendicular, Angle.

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Complete Geometry Problem 373

Level: High School, SAT Prep, College geometry

## Monday, October 26, 2009

### Problem 373: Square, Inscribed Circle, Diagonal, Perpendicular, Angle

Labels:
45 degrees,
angle,
circle,
diagonal,
inscribed,
perpendicular,
square

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Let O be the centre of the circle 1 and join EF. Since EAFO is a square, angle EFO=45.

ReplyDeleteThen, EAFH is concyclic, so that angle EFH=alpha. it is easy to find out that angle GOF=135 and hence angle OFH=22.5, so alpha=angle EFO-angle HFO=22.5

let o be the centre of circle join O,F and E,F then angle EFA=45 so angleEFO=45 and GO=OF so angle OGF=GFObut angleDOF=45 so angleOGF=angleGFO=45/2 so angleEFH=45- 45/2=45/2. and angle EAF+angle EHF=180 so E,H,F,A are concyclic. hence angle EAH=angle EFH 45/2

ReplyDeleteTr.s EOF and GOF are both isoceles O being the centre. Hence < HFE = 22.5 which is = to alpha considering that AEHF is cyclic

ReplyDeleteSumith Peiris

Moratuwa

Sri Lanka