Proposed Problem

Click the figure below to see the complete problem 296 about Intersecting Circles, Chord, Radius, Angle, Perpendicular.

See also:

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.

ReplyDelete