One angle of a triangle is

MATHEMATICS · Multi correct · A Level · Mathematics · Trigonometry · Trigonometry

Problem

60^\circ

, its area is

10\sqrt3

, and its perimeter is

20\,\mathrm{cm}

. If

a>b>c

, where

a

b

, and

c

are the side lengths opposite vertices

A

B

, and

C

, respectively, which of the following are correct? (1) Inradius of the triangle is

\sqrt3

. (2) Length of the longest side of the triangle is

7

. (3) Circumradius of the triangle is

\frac{7}{\sqrt3}

. (4) Radius of the largest escribed circle is

\frac{1}{12}