Marcia and Tamara are running a race. Marcia has run 4 kilometers. Tamara has completed the 3/4 of the race and is 2.5 kilometers ahead of Marcia. Write an equation that represents the relationship between the distances girl has run. Let k represent the total length of the race in kilometers.

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