In the triangle ABC, ab = AC, D point is on BC, and BD = ad, DC = AC

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• 1. In RT △ ABC, ∠ C = 90 °, AC = 5, BC = 12, if the circle with C as the center and R as the radius has a common point with the hypotenuse AB, the value range of R is obtained
• 2. In RT triangle ABC, angle B = 90 ', ab = 6 cm, BC = 8 cm. Point P starts from a and follows ab If points P and Q start from points a and B at the same time, then after a few seconds, the distance between two points P and Q is 53 cm? I use words to describe the symbols. Please read the meaning of the words clearly. Write the equation of one variable and degree
• 3. As shown in the figure, in △ ABC, ab = 8cm, BC = 16cm, point P starts from point a, moves along edge AB to point B at a speed of 2cm / s, and point Q starts from point B, moves along edge BC to point C at a speed of 4cm / s. if points P and Q start from point a and B at the same time, after a few seconds, △ PBQ is similar to △ ABC? Try to explain the reason
• 4. As shown in the figure, there is a right triangle paper with two right sides AC = 6cm and BC = 8cm. Now fold the right side AC along the straight line ad so that it falls on the hypotenuse AB and coincides with AE, then CD is equal to () A. 2cmB. 3cmC. 4cmD. 5cm
• 5. In RT △ ABC, ∠ C = 90 °, AC = 3cm, BC = 4cm, with C as the center, what is the positional relationship between the following r-radius circle and ab? r=2.4cm And R = 3cm
• 6. In RT △ ABC, what is the position relationship between the circle with C as the center and R as the radius and ab? （1）r=2cm （2）r=2.5cm （3）r=3cm
• 7. Let a straight line L with a slope of 1 pass through the focus of the parabola y ^ 2 = 4x and intersect with the parabola at two points a (x1, Y1); B (X2, Y2), then the vector OA × the vector ob=
• 8. A. B is two points on the parabola y ^ 2 = 2px (P > 0), which satisfies OA vertical ob (o is the origin), and proves that the straight line AB always passes a certain point How did you get the answer at the last step? I don't understand Or is there a better solution How to find (Y1 + Y2) * y = 2p (x-2p)?
• 9. Given that the straight line and parabola y ＾ 2 = 2px intersect at two points AB, and OA ⊥ ob, OD ⊥ AB intersect at D, D coordinate is (2,1), find the value of P First, I calculate the slope k of OD with the coordinates of point D, and then calculate the slope k 'of ab. because AB passes through D, we can know the equation of ab Then, the equation AB is substituted into the parabola, and the x 1 + x 2 and X 1x 2 are calculated by the Weida theorem Then, let a (x1, root 2px1), B (X2, root 2px2), calculate the algebraic formula of OA, OB length, because OA ⊥ ob, so the area is oaob / 2 Then calculate the length of AB section parabola, OD length and area abod / 2 with chord length formula Finally, because the two areas are equal, abod / 2 = oaob / 2, and then combined with vedadine to understand P
• 10. It is known that the straight line and parabola y & # 178; = 2px (P > 0) intersect at two points a and B, and OA ⊥ ob, OD ⊥ AB intersect at point D, and the coordinates of point D are (2,1), Let's find the value of P instead of a vector,
• 11. The positive △ a'b'c 'is obtained by rotating the positive △ ABC around point C clockwise for a certain angle=____
• 12. In △ ABC, the bisectors of ab ≠ AC, ABC and ACB intersect at O, and the bisectors of AB and AC intersect at e and F through o as EF ‖ BC (1) As shown in Figure 1, write out all the isosceles triangles in the graph. Guess: what is the relationship between EF and be, CF, and explain the reason. (2) as shown in Figure 2, the bisector Bo of ∠ ABC in △ ABC intersects the bisector Co of the outer angle of the triangle at O, and make OE ‖ BC at O, AB at e, and AC at F. is there any isosceles triangle in the graph? If so, point out them respectively. Write down the relationship between EF and be, CF, and explain the reason
• 13. As shown in the figure, in △ ABC, the bisectors of ∠ ABC and ∠ ACB intersect at point D, EF passes through point D and ef ‖ BC intersects AB at point E and AC at point F respectively. If AB = 10cm and AC = 8cm, calculate the perimeter of △ AEF
• 14. In △ ABC, bisectors of ∠ ABC and ∠ ACB intersect at point O, passing through point o as EF ‖ BC, AB at point E, AC at F, passing through point o as OD ⊥ AC at D, if od = 1cm , AE + AF = 7cm, calculate the area of △ AEF
• 15. The bisectors of angle ABC and angle ACB intersect at the point O EF, pass through the point O and parallel to BC, respectively, and intersect with ab AC at the point e F. the angle ABC is 50 degrees, and the angle ACB is 60 degrees Degree of BOC
• 16. In △ ABC and △ def, AB / de = BC / EF = Ca / FD = 2 / 3 and the perimeter difference is 15cm, the perimeter of these two triangles is calculated
• 17. A space vector represents the area of a triangle Attention! It's a space vector! It's not a plane vector! It's a solid geometry! How to use coordinates to represent triangle area? Is it the same as plane geometry?
• 18. Given that the standard deviation of x1, X2 and X3 is 2, what is the variance of 2x1 + 3, 2x2 + 3 and 2x3 + 3?
• 19. It is known that {an} and {BN} are arithmetic sequences with non-zero tolerance, then the sequence {an + BN}, {BN an}, {3an BN}, {5An + 4} How many of {anbn}, {an & sup2;} are arithmetic sequences? Ans: 4 Please help me~
• 20. Let FX = {[1 + SiNx + (SiNx) ^ 2] ^ 0.5 - (a + bsinx)} / (SiNx) ^ 2, and point x = 0 is the removable discontinuity point of F (x), find a, B The process should be more detailed