(1)
If the angles of a triangle are in a ratio 4 : 5 : 6, and the perimeter of the triangle is 100cm, find
若三角形的角的比例是 4 : 5 : 6, 且三角形的周长是 100cm, 求

(a) the radius of the circumscribe circle.
外接圆的半径，

(b) the greatest side of the triangle.
三角形的最大边。

(2)
Given that (a + b) : (b + c) : (c + a) = 10 : 15 : 11 and the area of the triangle ABC is

*** QuickLaTeX cannot compile formula:
\frac{3}{2}\sart{3}cm^2

*** Error message:
Undefined control sequence \sart.
leading text: $\frac{3}{2}\sart

. Calculate
已知(a + b) : (b + c) : (c + a) = 10 : 15 : 11 及三角形的面积是

*** QuickLaTeX cannot compile formula:
\frac{3}{2}\sart{3}cm^2

*** Error message:
Undefined control sequence \sart.
leading text: $\frac{3}{2}\sart

. . 计算

(a) the length of the largest side,
最大的边长，

(b) the radius of inscribe circle,
内切圆的半径

(c) the radius of circumscribe circle.
外接圆的半径

(3)
B = 60, b = 4, area = , find求

(a) a, c， (a > c)

(b) the radius of the inscribe circle,
内切圆半径，

(c) the radius of the circumscribe circle.
外接圆半径。

(4)

In Fig, the circle O is the circumscribe circle of ABC as well as the inscribe circle of PQR. If PQ = 10cm, QR = 12cm, RP = 14cm, find

图中，圆O 同时是 ABC 的外接圆以及 PQR 的内接圆. 若PQ = 10cm, QR = 12cm, RP = 14cm, 求

(a) the area of PQR
PQR 的面积

(b) the radius of the circle O
圆O 的半径

(c) P

(d) the length of the side AB.
AB 的边长。

(5)
Let the three sides of a triangle be a, b, c and A is a angle opposite to the side a.
If (b + c) : (c + a) : (a + b) = 6 : 4 : 5, and perimeter of ABC is , find

已知a, b, c 为一三角形的三边和 A 是 a 边所对的角. 若 (b + c) : (c + a) : (a + b) = 6 : 4 : 5, 及 ∆ABC 的周长为 , 求

(a) sinA : sinB : sinC,

(b)

*** QuickLaTeX cannot compile formula:
\angleA

*** Error message:
Undefined control sequence \angleA.
leading text: $\angleA

,

(c) the area of ABC,
ABC 的面积，

(d) radius of circumscribe circle of ABC
ABC 的外接圆半径，

(e) radius of inscribe circle of ABC.
ABC 的内切圆半径。

已知A, B 和 C 在圆O 上且弧 AB : 弧 BC : 弧 AC = 3 : 4 : 5, AB 边长是 , 计算

(a) the radius of circle O,
圆O 的半径，

(b) the area of ABC,
ABC 的面积

(c) the radius of the inscribe circle of ABC.
ABC 的内切圆半径

Given that s is a semi-perimeter of ABC and (s – a) : (s – b) : (s – c) = 7 : 2 : 1. Find the radius of the inscribe circle if the area of ABC is .

已知s 为 ABC 的半周长且(s – a) : (s – b) : (s – c) = 7 : 2 : 1. 若ABC 的面积是求内切圆半径。