As shown in the figure: AE is the bisector of ∠ BAC in square ABCD, AE intersects BD and BC at f and e respectively, AC and BD intersect at O, verification: of = 12ce
It is proved that: take the midpoint P of AE, connect OP, ∵ point O is the midpoint of AC, ∵ OP is the median line of △ ace, ∵ OP = 12ce, Op ∥ ad, ∵ OPF = ∵ ead = ∵ EAC + ∵ CAD = ∵ EAC + 45 ° and ∵ ONP = ∵ abd + ∵ BAE = ∵ BAE + 45 °, EAC =
RELATED INFORMATIONS
- 1. Known: as shown in the figure, EF is the median line of trapezoidal ABCD, AF bisector angle DAB verification: ad = 2ef There is no picture
- 2. It is known that in trapezoid ABCD, ab ∥ CD, ad = DC = BC = 4 ∠ DCB = 120 ° CE ⊥ AB, the area of AC ⊥ BC and trapezoid is calculated
- 3. The vertical line CE is drawn from the vertex C of rectangle ABCD to the diagonal BD, and the perpendicular foot is e. if CE is divided into two angles with ∠ C being 1:5, then ∠ ace=
- 4. As shown in the figure, AC ⊥ BC, ad ⊥ BD, ad = BC, CE ⊥ AB, DF ⊥ AB, perpendicular feet are e and f respectively, so, CE = DF?
- 5. As shown in the figure, ab | DC, ad | BC, points E and F are on AB and DC respectively, and be = DF, AF = CE
- 6. It is known that: as shown in the figure, AC bisects ∠ bad, CE ⊥ AB in E & nbsp; CF ⊥ ad in F, and BC = DC
- 7. As shown in the figure, ab = CD, DF ⊥ AC in F, be ⊥ AC in E, DF = be, verification: AF = CE
- 8. Known: as shown in the figure, points B, e, C, f are on the same line, ab = De, AC = DF, be = CF
- 9. Known: as shown in the figure, points B, e, C, f are on the same line, ab = De, AC = DF, be = CF
- 10. As shown in the figure, in △ ABC, D is the point on AB, DF intersects AC at e, de = Fe, AE = CE, what is the positional relationship between AB and CF? Prove your conclusion
- 11. As shown in the figure, in ▱ ABCD, if the bisector AE of ∠ bad intersects BC at e, ad = 6, EC = 2, then the length of CD=______ .
- 12. Find the normal vector of the plane passing through points a (0,0,0), B (1,4,0), C (0,2,0)
- 13. It is known that the vertex of the parabola is at the origin and the focus is the focus of the hyperbola x ^ 2 / 16-y ^ 2 / 9 = 1
- 14. The vertex of the parabola is at the origin of the coordinate, and the focus coincides with a focus of hyperbola Y / 5-x / 4 = 1
- 15. 1 2 3 4 5 =200 Adding addition, subtraction, multiplication and division to the left side of the equation can sum two numbers into one number, or add brackets, but the order cannot be changed to make the equation hold Example (1 + 23) * 4-5 = 91, but it is not equal to 200
- 16. 1995-1+2-3+4-5+… +1948-1949=______ .
- 17. 1995-1+2-3+4-5+… +1948-1949=______ .
- 18. Mathematical problems of plane rectangular coordinate system under seven "Monster eats peas" is a computer game. The symbols in the picture indicate the locations where the "monster" passes successively. If (1,2) is used to indicate the third location where the "monster" passes according to the route indicated by the arrow in the picture, can you show the other locations where the "monster" passes in the same way?
- 19. There are two points a (- 1,0) and B (1,0) on the plane, and point P is on the circle (x-3) 2 + (y-4) 2 = 4. Find ap2 There are two points a (- 1,0), B (1,0) on the plane, and point P is on the circle (x-3) 2 + (y-4) 2 = 4. Find the coordinates of point P when ap2 + bp2 takes the minimum value The equation of a circle is that the square of (x-3) plus the square of (y-4) equals 4 [2 is the square] What we need is also the square of AP plus the square of BP
- 20. For example, there are two points a (1,0) and B (- 1,0) on the plane of the graph, and the known equation of the circle is (x-3) ^ 2 + (y-4) ^ 2 = 2 ^ 2 Find the maximum area of ABP1 with a point p1 on the circle and find out the area