
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(D_{1},
D_{2}) = 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.
s_{a }
= ? 

Example:
The altitude of a triangle to the side a,
h_{a}
= 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, h_{a}
= 2 and A_{trapezium}
= A_{trangle}.
x_{ }
= ? 










Geometry
and use of trigonometry contents  A 



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