AD.BC Is the chord of two short points of diameter AB passing through the circle, and BD and AC intersect at point e. it is proved that AC × AE + BD × be = AB ^ 2

AD.BC Is the chord of two short points of diameter AB passing through the circle, and BD and AC intersect at point e. it is proved that AC × AE + BD × be = AB ^ 2

AC × AE = (AE + CE) × AE = AE & sup2; + CE × AE = ad & sup2; + de & sup2; + CE × AE, we can get BD × be = be & sup2; + be × de from intersection chord theorem, so AC × AE + BD × be = ad & sup2; + de & sup2; + 2be × De

Known: as shown in the figure, AE = CF, ∠ DAF = ∠ BCE, ad = CB
Q: is △ ADF congruent with △ CBE? Please explain the reason
If △ BEC is moved parallel along the direction of Ca edge, the following three graphs can be obtained. If the above conditions remain unchanged, is the conclusion still valid? Please explain the reason

Send out the picture

As shown in the figure, BD is the diameter of circle O, ab = AC, ad intersects BC with E, AE = 2, ed = 4. (1) prove that triangle Abe is similar to triangle ADB (2) find AB length (3) extend DB to F
(1) prove that the triangle Abe is similar to the triangle ADB. (2) find the length of AB (3) extend DB to f so that BF = Bo, connect FA, judge whether the straight line FA is tangent to the circle O, and explain the reason

(1) According to ab = AC, we can get ﹥ ABC = ﹥ C, by equivalent substitution, we can get ﹥ ABC = ﹥ D, and then we can prove ﹥ Abe ﹥ ADB. (2) according to ﹥ Abe ﹥ ADB, we can get the length of AB by using its corresponding edge proportion and substituting the known value. (3) connecting OA, we can get ﹥ bad = 90 ° according to the diameter of BD ⊙ o

If two points AB are symmetric about the origin, then their abscissa and ordinate

The abscissa and ordinate are opposite, such as a (x, y), then B (- x, - y)
On X-axis symmetry, such as a (x, y) then B (x, - y)
On Y-axis symmetry, such as a (x, y), then B (- x, y)

About X-axis symmetric point, abscissa, ordinate, about Y-axis symmetric point, abscissa, ordinate, about origin symmetric point

For example, a (3, - 4)
The point of x-axis symmetry is (3,4), the abscissa does not change, and the ordinate changes to the opposite number
For Y-axis symmetric points (- 3, - 4), the ordinate remains unchanged and the abscissa becomes the opposite number
For the symmetric point (- 3,4) of the origin, the vertical and horizontal coordinates become the opposite number

In the plane rectangular coordinate system, given that point a (2a-b, - 8) and point B (- 2, a + 3b) are symmetrical about the origin, then the value of a · B is______ ．

From the meaning of the question: 2a-b = 2, - 8 = - a-3b, the solution is: a = 2, B = 2. Therefore, the answer is: 4

As shown in the figure, in the plane rectangular coordinate system, O is the origin, point a is on the positive half axis of X axis, and point B is on the positive half axis of Y axis

(1) in quadratic function, let x = 0, y = 2, ∩ B (0,2), OB = 2oa, ∩ a (1,0), ∩ 0 = 1 + m + 2, M = - 3, ∩ analytic formula of quadratic function: y = x ^ 2-3x + 2, AC = ab, ∩ OAB + ∩ oba = 90 degree, ∩ BAC = 90 degree, ∩ OAB + ∩ MAC = 90 degree, ∩ oba = ≌ RT Δ OAB ≌ RT Δ MCA, ∩ cm = OA = 1, am = ob

In Cartesian coordinate system, the analytic expression of line L1 is y = 2X-4, line L2 passes through the origin, and line L2 and line L1 intersect at point P (- 2, a)
Try to find the value of A
How can (- 2, a) be regarded as the solution of a system of linear equations of two variables
3 line L1 and X axis intersect at a, can we find the area of the triangle apo? Try it
4 is there Diana on the line L1, so that the distance between M and x-axis, he and y-axis is equal? If there is a coordinate, there is no reason

1. Let L2 be y = KX, then the intersection coordinates are (4 / (2-k), 4K / (2-k)) 4 / (2-k) = - 2, so k = 4, so a = 4K / (2-k) = 42. It can be seen as a bivariate linear equation composed of two straight lines y = - 2XY = 2x-43. The coordinates of a point are (2,0) area s = OA * H (H is the Y coordinate of P) = 44

In Cartesian coordinate system, the analytic expression of line L1 is y = 2x-1, line L2 passes through the origin and L2 and line L1 intersect at point P (- 2, a). (1) try to find the value of a; (2) try to ask (- 2, a) what kind of solutions of binary linear equations can be seen; (3) suppose line L1 and X axis intersect at point a, can you find the area of △ apo? Try; (4) is there a point m on the line L1 so that the distance from the point m to the X and Y axes is equal? If it exists, find out the coordinate of point m; if it does not exist, explain the reason

(1) Substituting (- 2, a) into y = 2x-1, we can get: - 4-1 = a, and the solution is a = - 5. (2) we know from (1): point P (- 2, - 5); then the analytical expression of line L2 is y = 52X; therefore (- 2, a) can be regarded as the solution of binary linear equation system y = 2x − 1y = 52X. (3) line L1 intersects with X axis at point a (12, 0), so s

In Cartesian coordinates, the line L1 passes through points (2,3) and (- 1, - 3), the line L2 passes through the origin and intersects with the line L1 at point (- 2, a): (1) find the value of A

Let the analytic expression of line L1 be: y = KX + B. because line L1 passes through points (2,3) and (- 1, - 3), so 3 = 2K + B - 3 = - K + B, the solution is: k = 2, B = - 1, so L1: y = 2X - 1, because point (- 2, a) is on L1, so a = 2x (- 2) - 1 = - 5