Geometry - Triangle Problems and Solutions
      Triangle, solved problems, examples
Example:   In a right triangle the bisector of the angle a divides opposite leg to two segments, find the ratio between greater and smaller of segments. 
Solution:   Given, a.   x / y = ?
 
Example:   Into a right triangle inscribed is a circle. The point of contact divides the hypotenuse to segments whose lengths are 5 cm and 12 cm. Length of the shorter leg is? 
Solution:   Given,  c = 17 cm  then  a - r = 5 cm, b - r = 12 cm, and  b - a = 7 cm.   a = ?
 
Example:   Into an isosceles triangle, whose base length is 16 cm and equal sides of 10 cm each, is inscribed and then circumscribed a circle. Distance of their centers is?
Solution:   Given,  a = 16 cm and b = 10 cm.   d = ?
 
Example:   Legs of a right triangle are, a = 4 and b = 3, length of the angle bisector at the vertex A is?
Solution:   Given,  a = 4 and b = 3.   sa = ?
 
Example:   The altitude of a triangle to the side a, ha = 2 at what distance from the side a should be drawn a line parallel to a such that it divides the triangle to two parts of equal areas.
Solution:   Given,  ha = 2 and Atrapezium = Atrangle.   x = ?
 
Example:   Lengths of medians drawn from the vertices of acute angles of a right triangle are 7 cm and 4cm. Length of the hypotenuse is? 
Solution:   Given,  ma = 7 cm  and  mb = 4 cm.   c = ?
 
Example:   Given is a triangle with sides, b = 6 cm, c = 4 cm and the median from the vertex Bmb = 5 cm, find the area of the triangle.
Solution:  Given,  b = 6, c = 4 cm  and  mb = 5 cm.   AD = ?  Use of the cosine law.
 
Example:   Lengths of sides of a triangle are, a = 8 cm and b = 6 cm. How much is altitude hb to the side b greater than the altitude ha to the side a if the length of the altitude ha = 4 cm?
Solution:  Given,  a = 8 cm, b = 6 cm  and ha = 4 cm.   hb - ha = ?
 
Example:   The point of contact of incircle with radius 4 cm divides the side of a triangle to segments whose lengths are, 6 cm and 8 cm. The length of the biggest side of the triangle is? 
Solution:  Given,  r = 4 cm and a = 14 cm.   x = ?
 
Geometry and use of trigonometry contents - A
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