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(1)
If the angles of a triangle are in a ratio 4 : 5 : 6, and the perimeter of the triangle is 100cm, find

(a) the radius of the circumscribe circle.

(b) the greatest side of the triangle.

(a) 19.48cm

(b) 37.11cm

(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,

(b) the radius of inscribe circle,

(c) the radius of circumscribe circle.

(a) 4cm
(b) cm
(c) 2.02cm

(3)
B = 60, b = 4, area = , find求

(a) a, c， (a > c)

(b) the radius of the inscribe circle,

(c) the radius of the circumscribe circle.

(a) 4.38, 0.91

(b)  0.37

(c)   2.31

(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

(a) the area of PQR
PQR 的面积

(b) the radius of the circle O

(c) P

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

(a) 24cm

(b) 3.27cm

(c) 57.12

(d) 5.744cm

(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

(a) sinA : sinB : sinC,

(b)

*** QuickLaTeX cannot compile formula:
\angleA

*** Error message:
Undefined control sequence \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。

(a) 3 : 7 : 5

(b) 21.78

(c) 19.48 单位

(d) 7

(e) 1.5

(6)
Given that A, B and C are on circle O where curve AB : curve BC : curve AC = 3 : 4 : 5, the length AB is , then calculate

(a) the radius of circle O,

(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