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virtualanimosity
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geometry 9 02 Oct 2009, 11:29
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

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Q.
2 circles C(O,r) and C( O',r') intersect at 2 points A and B and O lies on C(O',r'). A tangent CD is drawn to the circle C(O',r') at A.Then

a. angle(OAC)= OAB
b. angle( OAB)=AO'O
c. angle (AO'B)=AOB



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orsang8
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geometry 9 05 Oct 2009, 12:26
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Where did you see this problem? It looks extremely difficult.
I hope someone post the answer and the explanation. I am curious now.
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jax91
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geometry 9 07 Oct 2009, 14:01
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virtualanimosity
Q.
2 circles C(O,r) and C( O',r') intersect at 2 points A and B and O lies on C(O',r'). A tangent CD is drawn to the circle C(O',r') at A.Then

a. angle(OAC)= OAB
b. angle( OAB)=AO'O
c. angle (AO'B)=AOB
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Here,

O'A=OO'=O'B (radiuses)

Also triangles AOO' and BOO' are identical.

so angle O'AO=AOO'=OBO'=BOO' = x

So OO'A = OO'B = 180-2x

angle O'AC=90 (tangent + radius)

So OAB= 90-x

Let AB and OO' intersect at E.

In triangle OAE, angle OEA=90.
Since <EOA = x, angle OAE=OAB=90-x

so OAB=OAC.



Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Problem Solving (PS) Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
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