Geometry - Triangle Problems and Solutions
      Triangle, solved problems, examples
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 = ?
 
Example:   A side of a triangle its angles, b = 30 and g = 45, find the area of the 
triangle.
Solution:  Given,  side a, b = 30 and g = 45.   AD = ?
 
Example:   The base of an isosceles triangle is 2 cm longer, and its equal sides 1 cm longer then the altitude to the base. The area of the triangle is?
Solution:  Given,   a = ha + 2  and  b = ha + 1.   AD = ?
 
Example:   A circle with the center at the center of an equilateral triangle intersects all three sides of the triangle to three equal parts each. Find the area of the parts of the triangle outside the circle if the side of the  triangle a = 6.
Solution:  Given,   a = 6.   A = ?
 
Example:   Lengths of sides of a right triangle are terms of an arithmetic progression with the difference 2, find the radius of incircle.
Solution:  Given,  a = xb = x + and  c = x + 4.   r = ?
 
Example:   A line parallel to the side AB, of a triangle ABC, divides the triangle to two parts of the same areas and intersects the side AC at the point A1 and the side BC at the point B1. If radii of incircles of triangles, ABC and A1B1C are at the same time legs of a right triangle whose hypotenuse length is 43, find the radius of the incircle of the triangle ABC.
Solution:
Geometry and use of trigonometry contents - A
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