Question

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

• A. $P:p=R:r$ only sometimes
• B. $P:p=R:r$ always
• C. $P:p=K:k$ only sometimes
• D. $R:r=K:k$ always
• E. $R:r=K:k$ only sometimes

Answer 1

The correct option is B $P:p=R:r$ always

Since the triangles are similar, we have $A:a=P:p=R:r=\sqrt{K}:\sqrt{k}$ always, so that (b) is the correct choice.