In the right triangle ABC, ∠ ACB = 90 ° and CD is the height on the edge of AB, ab = 13cm, BC = 12cm, AC = 5cm, Find the area of △ ABC and the length of CD

In the right triangle ABC, ∠ ACB = 90 ° and CD is the height on the edge of AB, ab = 13cm, BC = 12cm, AC = 5cm, Find the area of △ ABC and the length of CD

The area is equal to 12 * 5 / 2 = 30
cd=5*12/13=60/13

In the right triangle ABC, ∠ AGB = 90 °, CD is the height on AB side, ab = 13cm, BC = 12cm, AC = 5cm. Find the length of CD

Let ad = x, DB = y, CD = Z, then: x + y = AB = 13 (1) x * y = Z ^ 2 (2) Z ^ 2 + x ^ 2 = 5 ^ 2 = 25 (3) be replaced by (1) y = 13-x, (2) x (13-x) = Z ^ 2 = > 13x-x ^ 2 = Z ^ 2 = > x ^ 2 + Z ^ 2 = 13X by (3) Z ^ 2 + x ^ 2 = 5 ^ 2 = 25 13X = 25 = > x = 25 / 13z ^ 2 = 5 ^ 2 – (25 / 13) ^ 2 = (5 - (2

If AB = BC = CA = 3, then the volume of the ball is______ .

Let the radius of the ball be 2x
4x2=x2+（2
3 x
Three
2 × 3) 2, x = 1
The radius of the ball is r = 2
The volume of the ball is v = 4 π
3R3=32
3π．
So the answer is: 32
3π．

There are three ABC points on the sphere with a radius of 13 cm, ab = BC = AC = 12 cm. The distance from the center of the sphere to the section passing through these three points is calculated

In fact, the bottom of the problem is the length of the triangle,
If the length of the three sides is 13, find the distance from the top to the bottom,
Make a vertical line to the ground through the vertex. The perpendicular foot is O, connecting Ao,
According to the properties of the center of gravity of the triangle, Ao = 2
3×12sin60°＝4
Three
According to the known hypotenuse length of a right triangle is 13, a right angle side length is 4
3，
The required right angle side length is
132−(4
3)2＝
121=11，
That is, the distance from the center of the sphere to the section passing through the three points is 11cm

On a sphere with a radius of 13 cm, a, B, C points, ab = 6cm, BC = 8cm, CA = 10cm, find the distance from the center of the sphere to the plane ABC Please write the calculation process, thank you

Let the distance be H
From ab = 6cm, BC = 8cm, CA = 10cm, △ ABC is a right triangle
∵ the distance between O and a, B and C is equal
The projection o 'of the center of the sphere on the plane ABC must be the midpoint of the hypotenuse
Therefore, in RT △ oo'c, H = OO '= √ (169-25) = 12
Drawing letters on icons is easy to understand

There are three points a, B and C on the sphere, where AB = 18, BC = 24, AC = 30, and the distance from the center of the sphere to the plane ABC is half of the radius of the ball, then the radius of the ball is () A. 20 B. 30 C. 10 Three D. 15 Three

According to the title AB = 18, BC = 24, AC = 30, ∵ 182 + 242 = 302, we can see that the triangle is a right triangle,
The outer center of the triangle is the midpoint of AC, and the distance from the center of the sphere to the section is the distance between the center of the triangle and the outer center of the triangle,
Let the radius of the ball be r and the distance from the center of the ball to the plane where △ ABC is located is half of the radius of the ball,
So R2 = (1
2R）2+152，
R2 = 300,
∴R=10
3．
Therefore, C

Given that there are three points a, B and C on the sphere with radius 13, ab = 6, BC = 8, AC = 10, then the distance from the center of the sphere to the section ABC is () A. 12 B. 8 C. 6 D. 5

∵ there are three points a, B and C on the sphere with radius 13,
AB=6，BC=8，AC=10，62+82=102，
ν Δ ABC is RT △ ABC
∵ the projection m of the center of the sphere o in plane ABC is the center of the section circle,
⊥ m is the midpoint of AC and OM ⊥ AC
In RT △ OAM, OM=
OA2−AM2=12．
The distance from the center of the sphere to the plane ABC is 12
Therefore, a

A B C is a right triangle with two right sides BC = 7 and AC = 24. If there is a point P in △ ABC, and the distance from point P to each side is equal, then the distance is______ .

According to Pythagorean theorem, ab = 72 + 242 = 25, ∵ there is a point P in △ ABC, the distance from point P to each side is equal, ᙽ P is the center of the inscribed circle of △ ABC, and the tangent point is D, e, F, connecting PD, PE, PF, PA, PC, Pb, and the radius of the inscribed circle is r, then the formula of triangle area is 12 × AC × BC = 12 × AC ×

In the right triangle ABC, the angle c = 90 ° and the two right sides AC = 8, BC = 6. If there is a point P in the triangle, and the distance between the opposite sides is equal, then the distance is

If the whole area is 1 / 2 * 8 * 6 = 1 / 2 (8h + 6h + 10h), then H = 2
10 is the length of the oblique side calculated according to Pythagorean theorem

If △ ABC is a right triangle, both right sides are 6, there is a point P on the hypotenuse of the triangle, and the distance from the two right sides is equal, then the distance is equal to______ .

As shown in the figure, △ ABC is a right triangle, ∠ ABC = 90 °, ab = BC = 6,
∵ PD ⊥ AB in D, PE ⊥ BC in E, and PD = PE,
The point P is on the angular bisector of ABC,
∵AB=BC，
ν BP ⊥ AC (isosceles triangle with three lines in one), ∠ a = ∠ C = 45 °,
△ APB is an isosceles right triangle,
∴BD=AD=1
2AB=3．
So the answer is: 3