Geometry Problem
Click the figure below to see the complete problem 536 about Intersecting Circles, Chord, Perpendicular.
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Wednesday, November 3, 2010
Problem 536: Intersecting Circles, Chord, Perpendicular. Level: High School, SAT Prep, College Geometry
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extend AC to G on circle O, => BCG isoceles
ReplyDelete=> AD = DC + CG = BC + BC
Let E is the point of intersection of AC to circle O.
ReplyDeleteConnect OO’ and note that OO’ is the perpendicular bisector of AB
1. We have Angle(BEC)=angle (O’OA)
And angle(ACB)=2 *angle(O’OA)=angle(BEC)+angle(CBE)
So angle(CBE)=angle(O’OA)=angle(CBE)
Triangle BCE isosceles and CB=CE
2. Since AE is a chord of circle O so D is the midpoint of AE
We have Area(ADO)=Area(DOC)+Area(COE)
All above triangles have the same height so AD=DC+CE
Or AD=BC+CB
Peter Tran