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|Author:||fedana [ Tue Oct 16, 2012 4:38 pm ]|
|Post subject:||GMAT Geometry|
A circle is inscribed inside a right triangle as shown. If angle CAB = 60°, what is angle COE? (Note: Figure not drawn to scale.)
(D) Figure AEOC is a quadrilateral, so the sum of its interior angles must be 360°.
Therefore, angle COE = 360° – angle DAE – angle ACO – angle AEO.
We know that angle AEO is equal to 90° since the angle created by a radius and a tangent line is always 90°.
We also know that angle ACO is 45° because CDOF is a square and CO is its diagonal (CDOF is a square because all of its angles are 90° and DO = OF as radii).
Now we can solve for angle EOD:
Angle EOD = 360° – 60° – 45° – 90° = 165°.
The correct answer is D.
Why wouldn't angle ADO be 90 degrees (line DO is the radius and it hits a tangential line of the triangle)?
If it were 90 degrees then the answer would be 360 – 60 – 90 – 90 = 120 degrees
|Author:||Gennadiy [ Tue Oct 16, 2012 4:50 pm ]|
|Post subject:||Re: GMAT Geometry|
Why wouldn't angle ADO be 90 degrees (line DO is the radius and it hits a tangential line of the triangle)?The angle ADO is 90 degrees indeed.
If it were 90 degrees then the answer would be 360 – 60 – 90 – 90 = 120 degreesApparently, you have used angles in the quadrilateral ADOE and found the measure of the angle DOE. But the question asks for the angle COE, which equals angle DOE + angle DOC .
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