Circles problem

skeeter

Math Team
Jul 2011
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Texas
all I see is a circle with inscribed angles ... directions?
 
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skipjack

Forum Staff
Dec 2006
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The problem asks for the size of each lettered angle to be determined, but there is insufficient information in the diagram.

The diagram implies a + b = $60^\circ\!$.

If the lower left to upper right line segment is a diameter of the circle, a = $25^\circ\!$ and b = $35^\circ\!$.
 
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Mar 2020
6
0
UAE
The problem asks for the size of each lettered angle to be determined, but there is insufficient information in the diagram.

The diagram implies a + b = $60^\circ\!$.

If the lower left to upper right line segment is a diameter of the circle, a = $25^\circ\!$ and b = $35^\circ\!$.
The answer says a=35
b=25
But I don’t know why
 

skeeter

Math Team
Jul 2011
3,355
1,848
Texas
The answer says a=35
b=25
But I don’t know why
As stated by skipjack, if chord AB is a diameter, then $\angle{ACB} = 90^\circ \implies \angle{BAC} = 25^\circ$

The incribed angle marked $a$ and $\angle{BAC}$ intercept the same arc $\implies a = 25^\circ$. From there you can determine angle $b$ ...


inscribed_circle.jpg
 
Mar 2020
6
0
UAE
As stated by skipjack, if chord AB is a diameter, then $\angle{ACB} = 90^\circ \implies \angle{BAC} = 25^\circ$

The incribed angle marked $a$ and $\angle{BAC}$ intercept the same arc $\implies a = 25^\circ$. From there you can determine angle $b$ ...


View attachment 11101
I think there is something that was not stated in that question, but AB should have been stated to be the diameter, do you have explanation for that case ? (Nothing stated to be the diameter)
Thanks in advance
 

skipjack

Forum Staff
Dec 2006
21,472
2,466
Without the diameter being given, the most that can be shown is that $a + b = 60^\circ$ (as the angles of a triangle add to give $180^\circ$).
 
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