Right triangle ABC, AB is 40 cm long, BC is 10 cm long, square bdef is the largest square in the triangle, find the square area (please explain the thinking process in detail, and list the formula)

Let BD = de = EC = CB = x, then ad = ab-bd = 40-x. according to the proportional relation of triangle (triangle ade and triangle ABC): AD / AB = de / BC (40-x) / 40 = x / 10, the maximum side length x = 8 is obtained

A trapezoid, 9 cm in height and 16 cm in height, is divided into two parts A and B by a connecting line between a vertex and a middle point on the waist. The area ratio of a and already is 7:4

There are two cases: one is the top of the line, the other is the top of the line, the other is the bottom of the line

The numbers in the figure represent the area of two rectangles and a right triangle, and the area of the other triangle is______ ．

Because Ao × od = 16, OC × OE = 18, so Ao × OD × OC × OE = 16 × 18, and OD × OE = 6 × 2 = 12, so OA × OC = 16 × 18 △ 12 = 24, so the area of the other triangle is 24 △ 2 = 12, answer: the area of the other triangle is 12. So the answer is: 12

As shown in the figure, the area of the lower square is 8cm2, and how many square centimeters is the area of the circle?

Let the radius of the circle be r, then R2 = 8 square centimeter, 3.14 × 8 = 25.12 square centimeter; answer: the area of the circle is 25.12 square centimeter

To find a geometric figure of a circle in a mathematics book of grade three~
There's a RT △ ABC, AB, BC, CD whose lengths are a, B, C respectively. Find the length of the radius r of the inscribed circle (this seems to be the size or something, in short, it's almost the same), and draw the graph by yourself. It's very easy

What is this CD?
If the CD is AC
It's easy to remember that radius r = 1 / 2 (a + B + C)
It's like applying the congruence of triangles

Mathematics geometry problems in junior three (with pictures)
(picture address)
1. As shown in the figure, circle O is the inscribed circle of RT triangle ABC, with angle ACB = 90, ab = 13, AC = 12. Calculate the area of the shadow in the figure
2. If the height of BC side of triangle new ABC is ah, the length of BC is 30cm, the straight line De is parallel to BC, intersects AB and AC at points D and e respectively, and the semicircle with diameter de and BC are tangent to point F. if the area of semicircle is 18pai (circumference) cm ^ 2, the length of ah can be obtained. (this question is not attached)
3. As shown in the figure, it is known that the straight lines AB, BC and CD are tangent to the circle O at points e, F and g respectively, and ab is parallel to CD. If Bo = 6cm and co = 8cm, the lengths of BC, of and be + CG are calculated

1. The vertical lines of AB, AC and BC are made through O, and the vertical feet are D, e and f respectively
Yide BC = 5
Let od = OE = of = X
Then CF = CE = x
So BD = BF = 5-x, AE = ad = 12-x
So AB = 5-x + 12-x = 13
So x = 2
Triangle area = 5 * 12 / 2 = 30
Circle area = 4 Π
Shadow = 30-4 Π≈ 17.44

In the plane rectangular coordinate system, point O is the coordinate origin, and point P (m, - 1) (M > 0). Connect OP, and rotate the line OP 90 ° counterclockwise around point O to get the line OM, and point m is the vertex of the parabola y = AX2 + BX + C. (1) if M = 1, the parabola y = AX2 + BX + C passes through point (2,2), when 0 ≤ x ≤ 1, the value range of Y is obtained; (2) if the parabola y = AX2 + BX + C is known, the value range of Y is obtained The line AB intersects with the parabola y = AX2 + BX + C at point B. please judge the shape of △ BOM and explain the reason

(1) OP = om over point P (m, - 1) for PQ \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\1 ∵ parabolic When x = 0, y = 2, when x = 1, the value range of y = 1  y is 1 ≤ y ≤ 2. (2) ∵ point m (1, m) is the vertex of parabola y = AX2 + BX + C ∵ let y = a (x-1) 2 + M ∵ y = a (x-1) 2 + M = ax2-2ax + A + m ∵ B (0, a + m) and ∵ a (1, 0) ∵ the analytic expression of line AB is y=- (a + m) x + (a + m) to solve the system of equations y = AX2 − 2aX + A + my = - (a + m) x + (a + m), we get AX2 + (M-A) x = 0 ∵ there is only one intersection point between the straight line ab and the parabola y = AX2 + BX + C, and ∵ = (M-A) 2 = 0 ∵ M = a ∵ B (0, 2m). In RT ∵ Onm, from the Pythagorean theorem, om2 = Mn2 + on2 = 1 + M2 ∵ BM = om ∵ BOM is an isosceles triangle

There is an arc-shaped arch bridge. The width of the water surface under the bridge is 7.2m, and the vault is 2.4m higher than the horizontal plane. There is a cargo ship with a width of 3M, a square cabin top and a height of 2m higher than the water surface. Please judge whether the cargo ship can pass through the arch bridge smoothly? Give me your reasons

Let ob = OC = on = R, then od = (r-2.4) M. in RT △ BOD, according to Pythagorean theorem, R2 = (r-2.4) 2 + 3.62, r = 3.9. ∵ CD = 2.4m, the top of the cabin is square

As shown in the figure, in the plane rectangular coordinate system, the quadrilateral oabc is rectangular, and the coordinates of points a and B are (4,0), (4,3), respectively. The moving points m and N start from points o and B at the same time, and move at a speed of 1 unit per second, where point m moves along OA to terminal a, point n moves along BC to terminal C, passing through point n as NP ⊥ BC, intersecting AC to point P, connecting MP, when the two moving points move for T seconds. (1) point P The coordinates of are (expressed by algebraic formula containing T); (2) denote the area of △ MPa as s, and find the functional relationship between S and t (0 < T < 4); (3) when t= Second, s has the maximum value, the maximum value is__ (4) if the point q is on the y-axis, when s has a maximum and △ QaN is an isosceles triangle, the analytic expression of the line AQ is obtained

(1) (4-T, 3t4); (2) s = - 38t2 + 32t (0 < T < 4); (3) know from (2): S = - 38t2 + 32t = - 38 (T-2) 2 + 32, so when t = 2, Smax = 32; (4) know from (3), when s has the maximum value, t = 2, then n is at the midpoint of BC, as shown in the figure, let Q (0, y), ∫△ AOQ be a straight

How to draw mind map?

Now you're going to draw
Then tell you a point of view, the key of mind map is to draw by hand, not whether it looks good
Of course, if you want to improve, you can learn simple strokes, or contrast pictures

Right triangle ABC, AB is 40 cm long, BC is 10 cm long, square bdef is the largest square in the triangle, find the square area (please explain the thinking process in detail, and list the formula)