Help with This for Finding Solutions

[Vanillasyrup]

Homework Statement

From the moment of inertia of C2H2 and C2D2, I have to calculate the C≡C and C-H (C-D) bond lengths. I am confused on how to form the 2 simultaneous equations.

Relevant Equations

rH=
rC=

I really need help with this.

 

[TeethWhitener]

You need to at least show an attempt. What are the relevant equations?

 

[Vanillasyrup]

Thank you for your reply. This is what I got so far but I am very unsure.
IH=(mCrC^2 + mHrH^2)x 2
ID=(mCrC^2+ mDrH^2)x 2

 

[TeethWhitener]

What is the moment of inertia for a collection of point particles in general? Does this match what you have written?

Edit: my apologies. I see from the picture in OP how you have defined $r_H$ and $r_C$. Your moment of inertia equations are correct. What is the next step?