Can you use Sublime Chord spell slots to cast Bard spells known from your Bard class (or vice-versa)?

Question is lengthy, so I’ll put the question again but in full here:

Can you use Sublime Chord spell slots to cast Bard spells known from your Bard class (or vice-versa)?

Obviously the spell would have to be level 4-6.

We’ve got a bard looking at taking levels in Sublime Chord (he’s already a level 17 bard, so he has a lot of spells as a bard already), and Greater Mirror Image is an awesome spell. They are on both the Bard and Sor/Wiz lists at level 4.

My guess is no, and that the rules weren’t intended to work that way. We were saying it might be worth it to get it as a known spell for both classes. However, Bard and SC cast using the same mechanics, so it seems rather open to interpretation, and it seems strange to have to learn the same spell twice in this particular case (see below). I was wondering if anyone else had any resources or links to rulings on this.

The main argument is that from the perspective of almost any other set of 3.5 casting mechanics, you shouldn’t be able to do it. However in the case of Bard/SC, it seems unreasonable that you should have to learn a level 4 bard spell to cast it as a bard, then learn the same spell again (as a bard spell as required by the sublime chord spellcasting descriptor) just to cast it as a sublime chord.

If a circle with a diameter of 12 contains a chord of length 6 sqrt2, what is the length of the minor arc intercepted by the chord?

I’ve been stuck on this question for a while now… the main problem is that I don’t know the way I should draw it.

Should I draw it so that the diameter is perpendicular to the chord (so it can bisect the chord & its arc), or should I create an inscribed angle with the chord and diameter?

I tried both ways and I still have no idea how to even get an answer. Any help is much appreciated!