2AO is perpendicular to OB. A cat found a mouse in place B fleeing to the O hole in place A, so it chased the mouse at the same speed as the mouse. Please draw (or tell the process) the fastest way for a cat to stop a mouse. If one outer angle of an isosceles triangle is 80 degrees, then the degrees of its three inner angles are _ _ _ _.
If one outer angle of an isosceles triangle is 150, then the degrees of its three inner angles are _ _ _ _.
2. The two sides of an isosceles triangle are 4 cm and 9 cm respectively, so the circumference is _ _ _ _ cm.
3. The circumference of an isosceles triangle is 20, and the length of one side is 8, so the length of the other two sides is _ _ _ _ _.
4. In △ABC, AB = AC, ∠ A = 50, then ∠ B = _ _ _.
5. The acute angle between the heights of the two waists of an isosceles triangle is 70, so the degrees of the three internal angles of an isosceles triangle are _ _ _ _ _ _ _.
[6] It is known that the circumference of isosceles △ABC is equal to 24CM, and the difference between the base and the waist length is 3CM, then the base length of this triangle is _ _ _ _ _.
⒎ in triangle ABC, if ∠ A = 46 and ∠ B = 67, then △ABC is a _ _ _ _ triangle.
⒏ In ∠AOB, OP is its angular bisector, while PE⊥OA is in E and PF ⊥ OB is in F, then the relationship between PE and PF is _ _ _ _ _.
Position c, and briefly explain.
9.( 1) When k is what value, the solution of the equation set 2x-y=k+ 1 (1) is x = y.
(2)x+2y=2k
10. You should know that a= 1 and b=2.
Found1/ab+1[a+1] [b+1]+1[a+2] [b+2]+...............+1[a]
1 1. The area of Xiaoming's room is 10.8 square meters, and the floor of the room is just paved with 120 square bricks. What is the side length of each tile?
12. In the isosceles trapezoid ABCD, BC is parallel to AD, AB=DC, BC=2AD=4cm, BD is perpendicular to CD, CA is perpendicular to AB, and the vertical feet are respectively D, A and E are the midpoint of BC.
(1) Judge the shape of triangle ADE (briefly explain the reason). Find its circumference.
(2) Find the length of AB
(3) 3) Are AC and DE equally divided vertically? Please provide a justification for the answer.
13. Company A has 17 machines of the same model and 15 machines in A and B respectively, and now it needs to transport 18 machines in A and 14 machines in B. The transportation costs from A and B to A and B are as follows:
Party A (RMB/set) and Party B (RMB/set)
Adi 600 500
B di 400 800
(1) If it is transported from place A to station X in place A, find the functional relationship between the total cost y (yuan) required to complete the above transportation and station X (station).
(2) If the company designs the best transportation scheme with the lowest total cost, how much will it cost? Why?
14. A computer school conducted a typing speed test: given a certain number of words, unlimited time. Play in groups of four. A set of situations is as follows: if you complete this typing task alone, Party A needs 24 hours, Party B needs 20 hours, and Party C needs 16 hours, 12 hours (1). If Party A, Party B, Party D, Party A, Party B and Party D type in turn, and each person types for 65,438+0 hours, how long will it take to complete? (2) If you are a personal tutor, can you properly adjust the order of A, B, C and D mentioned in (1) and finish this typing task at least half an hour in advance? (Answer requirements: If you think you can't, you must give reasons; If you think it's ok, at least give a rotating order. How early can ice hockey finish typing? )
15 is known: a2+2a+b2-4b+5=0. Find the value of ab?
16 is known: a, b and c are positive rational numbers, 3a3+6a2b-3a2c-6abc=0 Proof: a = c.
17 Given that the rational numbers x, y and z satisfy (x2-xy+y2)2+(z+3)2=0, then x3+y3+z3 = _ _ _ _ _ _ _ _.
18 (a-b) n = _ _ _ _ _ (b-a) n (n is an odd number)
Two companies, 19A. B, they are all producing the same type of machines, namely 12 and 8. Now they sell 20 machines to Factory C and 10 machines to Factory D. It is known that the freight charges of Company A to Factory C and Factory D are 80 yuan 100 yuan and 60 yuan 120 yuan respectively. Write the cheapest. (3) What is the value of X, and the freight of A is more than that of B?
It is known that the point O is any point on the side AC of the triangle ABC (which does not coincide with AC), the intersection point O is a straight line l//BC, the straight line L intersects with the bisector of the angle BCA at point E, and intersects with the bisector of the angle BCA at point F.
1, OE and PF are equal? Why?
2. Where is the point O, and the quadrilateral AECF is a rectangle? Please provide a justification for the answer.