A jewelry maker is designing a crown. The crown must have at least 45 Gems using only emeralds Rubys and diamonds. the number Rubies must be 1 less than 3 times the number of emeralds. the number of diamonds must be 4 less than the number of rubies. which any quality cut the jewelry maker used to find the fewest number of emeralds X that can be placed on the crown

place r′ so that qr′ is parallel to the tangent.

now we get that ∠r′py=∠pr′q, where y is on the tangent, on the opposite side of p from x.

also, because of the symmetry, ∠r′py=∠qpx.

finally, note that no matter where we place r, as long as it's on the correct arc, we have ∠prq=∠pr′q.

stringing all these equalities together, we end up with ∠prq=∠qpx.

this picture will show how its going to look like.

hope this by jack monhen

lol   i know im kinda tired too