Proof: the sum of squares of the diagonals of a parallelogram is equal to twice the sum of squares of two adjacent sides

Let the short side of a parallelogram = a, the long side = B, the short diagonal = C, the long diagonal = D, the height on the long side = h, the distance between the intersection of the height on the long side and the long side to the near end of the long side = x, then there are respectively: H ^ 2 = a ^ 2-x ^ 2. (1) Note: H ^ 2 represents the square of H, H ^ 2 = D ^ 2 - (b

[geometric method] prove that the sum of squares of two diagonals of a parallelogram is equal to twice the sum of squares of two adjacent sides

Let the parallelogram ABCD, ab = CD = a, ad = BC = B. according to the cosine theorem, there are BD x BD = AB x AB + ad x ad - 2Ab x ad x cos a; AC x AC = AB x AB + BC x BC - 2Ab x ad x cos B; the sum of squares of two diagonals: BD x

If the lengths of the two right sides of a right triangle are 6 and 8 respectively, the length of the center line of the hypotenuse is______ ．

Given that the two right sides of a right triangle are 6 and 8, the length of the oblique side is 62 + 82 = 10, so the length of the middle line of the oblique side is 12 × 10 = 5, so the answer is 5

In RT △ ABC, if the lengths of right angles are known to be 6 and 8 respectively, then the median length on the hypotenuse is______ ．

According to Pythagorean theorem: ab = ac2 + BC2 = 62 + 82 = 10, ∵ CD is the middle line on the hypotenuse ab of the right triangle ACB, ∵ ACB = 90 °, ∵ CD = 12ab = 12 × 10 = 5 (the middle line on the hypotenuse of the right triangle is equal to half of the hypotenuse), so the answer is: 5

If the two sides of a right triangle are 6 and 8, then the circumcircle radius of the triangle is______

According to the Pythagorean theorem, the length of the hypotenuse of a right triangle is 8; the length of the hypotenuse of a right triangle is 62 + 82 = 10. Therefore, the circumcircle radius of the triangle is 4 or 5

5. If the lengths of the two right sides of a right triangle are 6 and 8 respectively, the radius of its circumcircle is________ Ask God for help

If the lengths of the two right sides of a right triangle are 6 and 8 respectively, what is the radius of the circumscribed circle? Because 6, 8 and 10 are a group of Pythagorean numbers, it means that this is a right triangle, and the side opposite 10 is the hypotenuse of the right triangle, and the center of the circumscribed circle of the right triangle is on the midpoint of the hypotenuse, so the diameter of the circumscribed circle is the length 10 of the hypotenuse, so the radius is 5

Given that the two right sides of a right triangle are 6 and 8 respectively, the circumscribed circle area of the triangle is The area of the inscribed circle is .

The radius of inscribed circle, according to "hook three strand four string five spring two", the spring is the diameter of inscribed circle. The radius is 2, which can be obtained by area method
The circumscribed area is 25 π
The area of the inscribed circle is 4 π

If the lengths of two right angles of a right triangle are known to be 6 and 8 respectively, the radius of its circumscribed circle is
If a chord of a circle divides the circle into two strings of degree 1:2, what is the degree of the central angle of the circle corresponding to this chord
Please draw a grass icon on the letter to answer
The second problem is to find the degree of circumference!

A chord of a circle divides the circle into two arcs with the degree of 1:2, and the center angle of the circle is 1 / 3 * 360 degrees = 120 degrees
If the radius of the circle is 5, and the radius of the circumscribed circle is half of the hypotenuse, which is 5, then the root 3 with chord length of 5 times can be obtained
According to the sine theorem, we can get 5 times root 3 / sin θ = 5 * 2 = 10, sin θ = 1 / 2 root 3, and the degree of circle angle is 60
Or according to the circle angle is 1 / 2 of the center angle, the degree of circle angle is 60

If the lengths of the two right sides of a right triangle are 6 and 8 respectively, then the radius of its circumcircle is The radius of the inscribed circle is ．

As shown in the figure, ∵ AC = 8, BC = 6, ∵ AB = 10, ∵ circumcircle radius is 5, let the radius of inscribed circle be r, ∵ CE = CF = R, ∵ ad = AF = 8-r, BD = be = 6-r, ∵ 6-r + 8-r = 10, the solution is r = 2

If the length of two right angles of a right triangle is 6 or 8, find the radius of its inscribed circle

Using the formula
Let r t △ ABC, C = 90 degrees, BC = a, AC = B, ab = C. the conclusion is that the radius of inscribed circle r = (a + B-C) / 2
The length of two right angles of a triangle is 6 and 8, then the oblique length is 10 according to Pythagorean theorem, and the radius is 2 according to the above formula

Proof: the sum of squares of the diagonals of a parallelogram is equal to twice the sum of squares of two adjacent sides