Knowing the parties of a triangle, it is possible to find the radius of the circle entered in it. The formula allowing to find radius, and then, length of a circle and the area of a circle and also other parameters is for this purpose used.
Instruction
1. Imagine an isosceles triangle in which the circle of unknown radius of R is entered. As the circle is inscribed in a triangle, but not described around it, all parties of this triangle are tangents to it. Height which is carried out from top of one corner perpendicularly to the basis coincides with a median of this triangle. It passes through radius inscribed circle.Sleduet to note that that triangle at which two sides are equal is called isosceles. Corners at the basis of this triangle have to be equal too. Such triangle can, at the same time, be entered in a circle and to describe about it.
2. At first find the unknown basis of a triangle. For this purpose, as it is already told above, carry out height from triangle top to its basis. Height will cross the center of a circle. If one of the parties of a triangle, for example, the party of CB is known at least, then the second party is equal to it as the triangle is isosceles. In this case, it is the party of AC. Find the third party which is the triangle basis on Pythagorean theorem: find c^2=a^2+a^2-2a^2*cosyУгол y between two equal parties that two corners are equal in an isosceles triangle. Respectively, the third corner is equal y=180 (a+b).
3. Having found all three parties of a triangle, pass to the solution of a task. The formula connecting lengths of the parties and radius looks as follows: r=(p-a)(p-b) (p-c)/p where p=a+b+c/2 is the sum of all parties halved or poluperimetr. If the isosceles triangle is entered in a circle, then it is in that case much easier to find circle radius. At knowledge of radius of a circle, it is possible to find such important parameters as the area of a circle and length of a circle. If in a task, on the contrary, circle radius is given - it is, in turn, a prerequisite to finding of the parties of a triangle. Having found the parties of a triangle, it is possible to calculate its area and perimeter. These calculations are widely applied in many engineering tasks. The planimetry is a basic science by means of which study more difficult geometrical calculations.