Why is circle 1 similar to circle 2? circle 1: center (2, 3) and radius 4 circle 2: center (2, 3) and radius 12

At a sale this week, a desk is being sold for $213. this is a 29% discount from the original price. what is the original price?

Elizabeth claims that the fourth root of 2 can be expressed as 2^m since (2^m)^n = 2. find the values of m and n for the case where elizabeth's claim is true.

In trapezoid abcd, ac is a diagonal and ∠abc≅∠acd. find ac if the lengths of the bases bc and ad are 12m and 27m respectively.