# Junior High School Olympiad # Introduction to the Olympic Mathematical Competition or Mathematical Olympiad, referred to as Olympiad. Olympic mathematics embodies the commonality between mathematics and the Olympic spirit: faster, higher and stronger. As an international competition, the International Mathematical Olympiad was put forward by international mathematical education experts, which exceeded the level of compulsory education in various countries and was much more difficult than the college entrance examination. Olympic Mathematics has a certain effect on teenagers' mental exercise, which can exercise their thinking and logic, and it plays a more profound role for students than ordinary mathematics. The following are the knowledge points of the second day of the Olympics: right triangle, welcome to read.

1 has a triangle with an angle of 90, which is called a right triangle.

A right triangle can be represented by Rt△, for example, right triangle ABC writes Rt△ABC.

Right triangle is a special kind of triangle, which has some special properties besides general triangle:

2. Nature

Property 1: The sum of squares of two right angles of a right triangle is equal to the square of the hypotenuse.

Property 2: In a right triangle, two acute angles are complementary.

Property 3: In a right triangle, the median line on the hypotenuse is equal to half of the hypotenuse. (that is, the outer center of a right triangle is located at the midpoint of the hypotenuse, and the radius of the circumscribed circle is R=C/2).

Property 4: The product of two right angles of a right triangle is equal to the product of the hypotenuse and the height of the hypotenuse.

Property 5: Projective Theorem

In a right triangle, the high line on the hypotenuse is the proportional average of the projection of two right angles on the hypotenuse, and each right angle is the proportional average of their projection on the hypotenuse.

∠ACB=90

CD⊥AB (4)ABCD=ACBC (usable area certificate)

(5) The radius of the circumscribed circle of the right triangle R= 1/2BC,

(6) The radius of the inscribed circle of the right triangle r= 1/2(AB+AC-BC) (formula1);

R=AB*AC/(AB+BC+CA) (Formula 2)

Property 6: In a right triangle, if there is an acute angle equal to 30, then the right side it faces is equal to half of the hypotenuse;

In a right triangle, if there is a right-angled side equal to half of the hypotenuse, then the acute angle of this right-angled side is equal to 30.