Can someone please help with this Geometry problem? I’m stuck.

[The Velociraptors]

I tried to draw triangles and use the Pythagorean theorem, but I got nowhere, and still couldn’t figure out first if AB=CD because if these to chords are equal, the arcs must be to.

 

[Deleted member 4993]

View attachment 20472I tried to draw triangles and use the Pythagorean theorem, but I got nowhere, and still couldn’t figure out first if AB=CD because if these to chords are equal, the arcs must be to.

Join ED.

What is the length of ED?

What is the length of GD?

What is the length of CD?

 

[pka]

If the two arcs are equal in length the the subtending cords are equal in length.
\(F~\&~G\) are the midpoints of their cords.
Consider the right triangles \(\Delta FAE~\&~\Delta GCE\)

 

[The Velociraptors]

Join ED.

What is the length of ED?

What is the length of GD?

What is the length of CD?

How should I find the lengths of GD or the hypotenuse if I only have one side? I cannot even use SohCahToa because I don’t have theta.

 

[The Velociraptors]

If the two arcs are equal in length the the subtending cords are equal in length.
\(F~\&~G\) are the midpoints of their cords.
Consider the right triangles \(\Delta FAE~\&~\Delta GCE\)

But even then, you only have the lengths of AF which is 20 and EG which is 7. I only have one side on each triangle, what do I do then? There is no theta or additional side lengths.

 

[Deleted member 4993]

How should I find the lengths of GD or the hypotenuse if I only have one side? I cannot even use SohCahToa because I don’t have theta.

Look at the figure carefully.

ED = radius = 25 = hypotenuse.....

 

[pka]

But even then, you only have the lengths of AF which is 20 and EG which is 7. I only have one side on each triangle, what do I do then? There is no theta or additional side lengths.

\(FA^2+FE^2=25^2~\&~GC^2+EG^2=25^2\) Now what?

 

[The Velociraptors]

Look at the figure carefully.

ED = radius = 25 = hypotenuse.....

Oh, ok. Using Pythagorean theorem, I get 24, so length of CD=48 meaning arcs aren’t equal. Thanks!

 

[The Velociraptors]

\(FA^2+FE^2=25^2~\&~GC^2+EG^2=25^2\) Now what?

For length of FE, I get 15, while EG is 7. GC is 24 meaning CD is 48. They cannot be equal. Thanks!