Need help proving these Geometry questions

[sosolil]

Dear community,

I need help proving those 3 conclusions. Please see the attached file. Here is what's given:
1. AOB = DCE = 90˚
2. OC cut through AOB evenly

We need to prove the following to be true:
1. CD = CE
2. OD + OE = √2 OC
3. S∆COD + S∆COE = 1/2 OC²

Thank you so much in advance!

 

[lev888]

Dear community,

I need help proving those 3 conclusions. Please see the attached file. Here is what's given:
1. AOB = DCE = 90˚
2. OC cut through AOB evenly

We need to prove the following to be true:
1. CD = CE
2. OD + OE = √2 OC
3. S∆COD + S∆COE = 1/2 OC²

Thank you so much in advance!

Draw 2 segments from C and consider 2 resulting triangles.

 

[sosolil]

Draw 2 segments from C and consider 2 resulting triangles.

Can you please be more specific? Thank you so much!

 

[lex]

 

[sosolil]

View attachment 26482

Thank you so much!!

 

[lex]

Glad you were able to complete it.