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| Geometry
- Triangle Problems and Solutions |
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Triangle, solved problems, examples |
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| 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 = ? |
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| 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
= ? |
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| 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
= ? |
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| 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
= ? |
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| 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
= ? |
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| 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
= ? |
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| Example:
Given is a triangle with sides,
b
= 6 cm, c
= 4 cm and the
median from the vertex
B, mb
= 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. |
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| 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 =
? |
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| 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
=
? |
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| Geometry
and use of trigonometry contents - A |
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| Copyright
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