Geometry - Triangle Problems and Solutions
Triangle, solved problems, examples
Example:   Lengths of sides of a triangle are in the proportion 9 : 10 : 17, find the radius of the incircle if the difference of the longest and the shortest side is 16 cm.
Solution:   Given,  a : b : = 9 : 10 : 17 and  c - a = 16 cm.  r = ?
Example:   The side AB of a triangle ABC is 9 cm long. Sides, AC and BC, form on a line l, which is parallel to side AB, the segment 3 cm long. If the distance of the vertex C from the line l is 3 cm, find the distance of the line l from the side AB.
Solution:   As shown triangles are similar following proportion must hold,

 9 : 3 = (3 + x) : 3 3 · (3 + x) = 3 · 9 3 + x = 9 x = 6 cm.
Example:   One leg and the hypotenuse of a right triangle are in relation 3 : 5, the perimeter of the triangle is 16 cm, find the area of the triangle.
Solution:   Given,  a : = 3 : 5 and  = 36 cm.  A = ?
Example:   In a circle of radius R inscribed is a right triangle whose area is 96 and the sum of legs 28 cm, find the radius R.
Solution:   Given,  A = 96 cm2 and  a + b = 28 cm.   R = ?
Example:   In a right triangle with hypotenuse c = 10 cm inscribed is a circle of radius r = 2 cm, area of the triangle is?
Solution:   Given,  c = 10 cm and  r = 2 cm.   AD = ?
Example:   If the ratio between angles in a triangle a : g = 1/6 : 1/8 and b : g = 1/3 : 1/2 then, the smallest angle in the triangle is?
Solution:  Given,  a : g = 1/6 : 1/8 and b : g = 1/3 : 1/2.    a, b and g = ?
Geometry and use of trigonometry contents - A