1960 AMC 12 Question 15 - thichhoctoan.com

Question 15

Triangle I is equilateral with side $A,$ perimeter $P,$ area $K,$ and circumradius $R$ (radius of the circumscribed circle). Triangle II is equilateral with side $a,$ perimeter $p,$ area $k,$ and circumradius $r.$ If $A$ is different from $a,$ then:

$P:p=R:r$ only sometimes
$P:p=R:r$ always
$P:p=K:k$ only sometimes
$R:r=K:k$ always
$R:r=K:k$ only sometimes