Proposed Problem
Click the figure below to see the complete problem 296 about Intersecting Circles, Chord, Radius, Angle, Perpendicular.
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Complete Problem 296
Collection of Geometry Problems
Level: High School, SAT Prep, College geometry
Wednesday, June 3, 2009
Problem 296: Intersecting Circles, Chord, Radius, Angle, Perpendicular
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Join OB and produce OC to DE at a point F.
ReplyDeleteLet angle OBC=y,
Then angle COB=180-2y
angle BAC=90-y=angle BED
Also, angle ECF=y
So, angle EFC=90, OC is perpendicular to DE
Let < EDA = @ then @ = < ABE = < AOC /2 hence < ACO = 90 - @ hence OC is perpendicular to DE
ReplyDeleteSumith Peiris
Moratuwa
Sri Lanka
See diagram here.
ReplyDeleteLet AB and DE intersect in F and OQ and circle O intersect in G
Since AB ⊥ OQ , OC ⊥ DE ⇔ ∠COQ = ∠BFD
But ∠BFD = ∠BAD - ∠ADF = ∠BAC - ∠ABC
Since A and B are symmetric versus OG, ∠BAC - ∠ABC = 2. ∠CAG = ∠COQ QED
The correct link to the diagram is here.
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