English has $6$ letters that can be vowels. this includes y, which can be either a consonant or a vowel; for this problem, we'll consider y a vowel. the other $20$ english letters are always consonants. how many two-letter "words" can we make from these letters if we are required to use at least one vowel? (we aren't limited to words that have an actual meaning in english. thus, for this problem, we'll include nonsense "words" like qo, xy, and uz.)

isocolese triangle

we know that the line connect a and b is the hyptonuse

so first find the hypotonuse length using the distance formula, call the length c

since it is an isocolese triangle, the lengths of the legs are the same

using pythagorean theorem,

in this case, a=b since isocolese triangle so we get

or

we can find c so we can find the distances

we know that if we draw 2 circles, each has center at a and b, and find where they intersect, we can the 2 possible locations for c

if a has center at (xa,ya) and b has center at (xb,yb), then we can solve where

and

intersect to find where they intersect

i'm not going to put an example because i have to go to class. i hope this explanation is enough