
Geometry
 Triangle Problems and Solutions 


Triangle, solved problems, examples 





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_{ }
= ? 


Example:
Lengths of medians drawn from the vertices of acute angles of a right triangle are
7
cm and 4
cm. Length of the
hypotenuse is? 
Solution:
Given, m_{a}
= 7 cm
and m_{b}
= 4 cm.
c_{ }
= ? 


Example:
Given is a triangle with sides,
b
= 6 cm, c
= 4 cm and the
median from the vertex
B, m_{b}
= 5 cm, find the area of
the triangle. 
Solution: Given,
b = 6,
c =
4 cm
and m_{b}
= 5 cm.
A_{D}
=
? Use of the cosine law. 

Example:
Lengths of sides of a triangle are, a =
8 cm and b =
6 cm. How much is altitude
h_{b}
to the side b greater than the
altitude h_{a}
to the side a
if the length of the altitude h_{a} =
4 cm? 
Solution: Given,
a = 8 cm,
b = 6
cm and h_{a} =
4 cm.
h_{b}

h_{a} =
? 

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°.
A_{D}
=
? 










Geometry
and use of trigonometry contents  A 



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