# Circles problem

#### Seiko

Can you help me with this ?!

#### skeeter

Math Team
all I see is a circle with inscribed angles ... directions?

• Seiko

#### skipjack

Forum Staff
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 = $35^\circ\!$.

• Seiko

#### Seiko

Find angle a and b

#### Seiko

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 = $35^\circ\!$.
b=25
But I don’t know why

Math Team

#### Seiko

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)

#### skipjack

Forum Staff
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 $180^\circ$).

• Seiko

#### Seiko

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 $180^\circ$).
Thanks a million