Let D and E be the points on the sides AB and BC of the triangle ABC, ad = 1 / 2Ab and be = 2 / 3bC. If de = in 1ab + in 2Ac, then in 1 + in 2 =? (both in 1 and in 2 in the title denote symbols,

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• 1. As shown in the figure, known isosceles △ ABC, AC = BC = 10, ab = 12, take BC as diameter, make ⊙ o intersection AB point D, intersection AC at point G, DF ⊥ AC, perpendicular foot is f, intersection CB extension line at point E. (1) prove: straight line ef is tangent line of ⊙ o; (2) find the value of sin ∠ a
• 2. As shown in the figure, D, e and F are respectively the midpoint of △ ABC, G is the midpoint of AE, and be intersects DF and DG at P and Q, then PQ: be=______ ．
• 3. As shown in the figure, in △ ABC, ∠ ACB = 90 °, AC = BC, point D is the midpoint of AB, AE = CF
• 4. As shown in the figure, △ ABC, ad is the midline, AE is the bisector of angles, CF ⊥ AE is f, ab = 5, AC = 2, find the length of DF
• 5. In the rectangular coordinate system with o as the origin, point a (4, - 3) is the right angle vertex of △ OAB. It is known that | ab | = 2 | OA |, and the ordinate of point B is greater than 0 1. Find the coordinates of vector ab 2. Find the equation of circle X & # 178; - 6y + Y & # 178; + 2Y = 0 with respect to the circle with OB symmetry
• 6. In the rectangular coordinate system, a (4, - 3) is the right angle vertex of OAB, and / AB / = 2 / OA /, the coordinates of vector AB are obtained //Represents absolute value, OAB is triangle
• 7. In the rectangular coordinate system with o as the origin, point a (4, - 3) is the right angle vertex of △ OAB In the rectangular coordinate system with o as the origin, point a (4, - 3) is the right angle vertex of △ OAB. It is known that | ab | = 2 | ab |, and the ordinate of point B is greater than zero Find the cosine value of the obtuse angle formed by the middle line on the two right angle sides of RT △ OAB It's a vector that can't be typed
• 8. There is a RT triangle ABC, BC = 2, AC = radical 3, ab = 1. Put it in the rectangular coordinate system, BC is on the x-axis, and the right angle vertex is on the y = radical 3 / X image, and find the coordinates of point C
• 9. In RT △ ABC, if the hypotenuse AB = 5 and the right angle BC = 5, then the area of △ ABC is______ ．
• 10. There is a RT △ ABC, a = 90 °, B = 60 ° and ab = 1, which is placed in the rectangular coordinate system Let the hypotenuse BC be on the x-axis and the right angle vertex a be on the inverse scale function y = radical 3 / x, and calculate the coordinate of point C (I will solve this problem, and the key is the next one). If we change the conditional hypotenuse BC on the x-axis to hypotenuse BC on the coordinate axis and point a on the image y = radical 3 / x, then calculate the coordinate of point C If it's OK, I'll give you extra points and help me solve it by next Monday
• 11. In RT triangle ABC, if ∠ C = 90 °, AC = 6, BC = 8, and G is the center of gravity of △ ABC, then CG =? RT
• 12. As shown in the figure, in RT △ ABC, ∠ ACB = 90 °, ab = 10, BC = 8, point d moves on BC (does not move to B, c), de ‖ AC, intersects AB with E, let BD = x, the area of △ ade is y. (1) find the functional relationship between Y and X and the value range of independent variable x; (2) when x is the value, the area of △ ade is the largest? What is the maximum area?
• 13. As shown in the figure, in RT △ ABC, ∠ a = 90 °, ab = AC = 2, point D is the midpoint of BC side, point E is a moving point on AB side (not coincident with a and b), DF ⊥ de intersects AC at F Let be = x, FC = y （1）DE=DF (2) The functional relation of Y with respect to X and the definition field of X are written out (3) When writing the value of X, EF / / BC
• 14. As shown in the figure, △ ABC and △ ade are equilateral triangles, and point D is on BC, CF ‖ de intersects AB with F. please explain the size relationship between CF and de
• 15. As shown in the figure, △ ABC is an isosceles right triangle, D is the midpoint of AB, ab = 2, sector ADG and BDH are 14 times of the circle with a and B as the center, ad and BD as the radius respectively, then the area of shadow part is______ ．
• 16. As shown in the figure, △ ABC is an isosceles right triangle, D is the midpoint of AB, ab = 2, and the center angles of sector ADG and BDH are all equal to 90 degrees
• 17. In RT △ ABC, ∠ C = 90 °, AC = 8, BC = 6, two equal circles ⊙ a, ⊙ B are circumscribed, then the sum of the areas of the two sectors (that is, the shadow part) in the figure is () A. 254πB. 258πC. 2516πD. 2532π
• 18. In order to cut the next circle on the iron sheet of a right triangle, ab = 60cm and BC = 80cm are known In order to make full use of this piece of iron, the diameter of the cut disc should be as large as possible How to cut? What is the maximum diameter of this circle?
• 19. As shown in the figure, C is the midpoint of line AB and D is the midpoint of line AC. given that the sum of the lengths of all line segments in the figure is 26, the length of line AC is calculated A———D———C——————B Use because so answer
• 20. Given that point C is a point on line AB and point D is the midpoint of line BC, the sum of the lengths of all line segments in the graph is 23, Connect the above problem: the length of AC and BC are both positive integers