Geometry - Triangle Problems and Solutions
      Triangle, solved problems, examples
Example:   Sides of a triangle, a = 13, b = 14 and c = 15, find the radius of the circle center of which lies on the side c and which touches sides, a and b.
Solution:   Given,  a = 13, b = 14 and c = 15.  r = ?
Example:   To a circle of radius 30 cm, from a point distant 50 cm from the circle center, drown are both tangents. Find the distance between tangents.
Solution:   Given,  r = 30 cm and OS = 50 cm.   d(D1, D2) = d = ?
Example:   Angles of a triangle ABC, which lay at the side AB, are 70 and 80, if O is the intersection of altitudes of the triangle and d angle (AOB) then, the sind is?
Solution:   Given, a = 70 and b = 80.   sin d = ?
Example:   Around a square with the side a circumscribed is an equilateral triangle with the altitude h and the base coincident with the side of the square. Find the side of the equilateral triangle. 
Solution:   Given, a and  h.   x = ?
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 = ?
Geometry and use of trigonometry contents - A
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