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markosheehan
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View attachment 6471im trying to use angles on the same arc theorem
Yes, the same arc theorem will certainly come into it. I suggest that you draw the lines $AL$ and $BC$ in the diagram, and then look for an external angle of the triangle $BCD$.markosheehan said:
That's right! Angle $CBL$ is an external angle of the triangle $BCD$, so it is the sum of the two opposite angles.markosheehan said:
The Using Angles on the Same Arc Theorem is a geometric theorem that states that angles inscribed in the same arc of a circle are equal.
This theorem is useful in geometry as it helps to solve problems involving angles and arcs on a circle. It can also be used to prove other theorems and geometric properties.
The theorem can only be applied when two or more angles are inscribed in the same arc of a circle. The angles must also be formed by intersecting chords, secants, or tangents on the circle.
Yes, the theorem can be extended to any number of angles as long as they are inscribed in the same arc of a circle.
The theorem can be proven using the properties of inscribed angles and the central angle theorem. By constructing a triangle with the inscribed angles, it can be shown that all angles are equal and therefore the theorem holds true.
