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The ratio of inscribed circle radius to circumscribed circle radius of triangles with side lengths of 3, 4 and 5 is () A. 1：5 B. 2：5 C. 3：5 D. 4：5
Let the radius of the inscribed circle of the right triangle be r,
∵ the side lengths are 3, 4 and 5 respectively,
∴3-r+4-r=5，
The solution is r = 1, that is, the radius of the inscribed circle is 1;
∵ the radius of the circumscribed circle is 5
2，
The ratio of inscribed circle radius to circumscribed circle radius is 1:5
2=2：5．
Therefore, B
A triangle has an angle of 60 degrees. If the lengths of both sides of the angle are 8 and 5 respectively, its inscribed circle area is
By the cosine theorem,
c^2=a^2+b^2-2abcos60=49,
c=7,
Let the radius of the inscribed circle be r,
Triangle area = absin60 / 2 = 10 √ 3
（a+b+c）r/2=10√3,
r=√3,
Inscribed circle area = 3 Π
What is the relationship between the inscribed circle of a triangle and the triangle (side length, area, etc.)
Area of triangle s = (1 / 2) r (a + B + C)
As shown in the figure: the three sides of △ ABC are a, B and C respectively, and the radius of the inscribed circle is R. then s △ = (1 / 2) r (a + B + C)
It is proved that the three tangent points are D, e and f respectively, and ad = AF = x, BD = be = y, CE = CF = Z
It can be proved by triangular area formula
How to find the area of the inscribed circle of a triangle? Known condition: length of three sides of triangle What is the relationship between the area of a triangle and the radius of the inscribed circle?
Helen formula: square of triangle area = P (P-A) (P-B) (P-C) P = 1 / 2 (a + B + C)
R of inscribed circle = 2 * area of triangle / perimeter of triangle
The area of the inscribed circle = π times the square of R
In triangular ABC, ab = 15, BC = 14, AC = 13, find the area of triangular ABC Tip: make a high on one side
There are two ways to solve this problem
1: Make the height: (for example, the height on the edge of BC, the vertical point is d), and let BD length be x, then DC is 14-x
Then the Pythagorean theorem is used to find the two expressions of AD, form the equation, solve the equation to get x, and then find the high ad
2: Cosine theorem: use the cosine theorem to find any internal angle of the triangle, and then s = 0.5 × Side length a × Side length b × Sin (angle between two sides)
As shown in the figure, in RT triangle ABC, ∠ C = 90 °, ∠ a = 15 °, BC = 1, calculate the area of triangle ABC
Make the vertical bisector of AB and intersect AC at point D
If BD is connected, DB = Da
∵∠A=15º
∴∠DBA=15º、∠BDC=30º
∵BC=1
∴DA=DB=2、CD=√3
∴S Δ ABC=(2+√3)/2=1+√3/2
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