Is there any connection between junior three and junior two

I don't think the connection is very big. After all, the difficulty of grade three is much higher than that of grade one and grade two. I just graduated from grade three this year. Grade three is similar to triangle, quadratic function is the key point, trigonometric function and circle must be clear about the concept

Known: for a rectangular clock, the top and bottom are long, the left and right are wide, 12.3.6.9 four points are on the midpoint of the four sides, 2 is on the vertex in the middle of 12.3, then what is the degree of angle ∠ 12o2? (o is the intersection of two diagonals)
There seems to be no condition for how to prove it

The clock goes 360 / 12 degrees in an hour, which is 30 degrees. That's right

Solving mathematical inequality solving inequality | x ∧ 2-5x | ≤ 6

|x^2-5x|≤6,
The square of both sides is (x ^ 2-5x) ^ 2 ≤ 36,
The term is shifted, the factor is decomposed, and the result is obtained
（x-2)(x-3)(x+1)(x-6)≤0,
From the root method of order axis, we can get - 1 ≤ x ≤ 2, or 3 ≤ x ≤ 6

Is there a formula for finding the tangent of a circle through a point outside the circle?
Note that it is a point outside the circle, not a point on the circle
What I ask is not the method of finding, but whether there is a formula for the coordinates of a given point and the general equation of a circle that can be found quickly

Let the equation of circle be (x + a) ^ 2 + (y + a) ^ 2 = R ^ 2
Let the known point be (m, n) and the tangent point be (T, s)
(t-a)^2+(s-b)^2=r^2
Root [(M-A) ^ 2 + (N-B) ^ 2] - root [(M-T) ^ 2 + (N-S) ^ 2] = R
Two equations, and only two unknowns, t and s, can be solved
Because the tangent equation of a circle goes through (m, n), (T, s),
Therefore, the tangent equation (two-point formula) of a circle can be obtained
The formula can be deduced
It should not be. It is required that the linear equation, knowing a point, must start with the slope, and then find a point, and another point must be combined with the equation of circle, as mentioned above

For example, what is the tangent equation of circle x ^ 2 + y ^ 2-4x = 0 at point P (1, radical 3)?
Who knows the formula of tangent length equation from point to circle?

Because x ^ 2 + y ^ 2-4x = 0,
So x ^ 2-4x + 4 + y ^ 2 = 4,
So (X-2) ^ 2 + y ^ 2 = 2 ^ 2,
Obviously, the center of the circle is (2,0),
So let the analytic expression of the line OP be y = KX + B,
There are
2k+b=0,
k+b=√3,
The solution is k = - 3, B = 2 √ 3,
So the analytic expression of OP is y = - √ 3x + 2 √ 3,
Its slope k = - 3,
Because the tangent is perpendicular to the radius,
So K '= √ 3 / 3, (the product of the slopes of two lines perpendicular to each other is - 1)
So let the analytic expression of tangent be y = √ 3x / 3 + B ',
Because P (1, √ 3) is on the tangent,
So there is √ 3 / 3 + B '= √ 3,
So B '= 2 √ 3 / 3,
So y = √ 3x / 3 + 2 √ 3 / 3,
That is, the analytic formula of tangent is √ 3x-3y + 2 √ 3 = 0

The tangent equation and proof method of the general formula of passing through a point on a circle

Let the equation (x-a) ^ 2 + (y-b) ^ 2 = R ^ 2, P (x0, Y0) be a point on the circle, then the tangent equation of the circle is: (x0-a) (x-a) + (y0-b) (y-b) = R ^ 2. Prove that: ∵ p (x0, Y0) is a point on the circle ∵ (x0-a) ^ 2 + (y0-b) ^ 2 = R ^ 2. To prove that the tangent equation of the circle is: (x0-a) (x-a) + (y0-b) (y-b) = R ^ 2, only prove that

The tangent chord equation of a circle
If a point m (A0, B0) outside the circle (x ^ 2 + y ^ 2 = R ^ 2) leads to two tangents of the circle, and the two tangents are a and B, then the equation of the line where a and B are located is also A0 * x + B0 * y = R ^ 2

Let a (x1, Y1) and B (X2, Y2) be: the tangent equation passing through point a is: X1X + y1y = R & # 178; the tangent equation passing through point B is: X1X + Y2Y = R & # 178; since point (A0, B0) is on the tangent, then: x0x1 + y0y1 = R & # 178;, x0x2 + y0y2 = R & # 178; the equations show that: points a (x1, Y1) and B (X2, Y2) are on the straight line

Proof of tangent equation of circle
A point outside the circle P (x0, Y0) leads a tangent line to the circle. The tangent equation is xX0 + yy0 = R ^ 2. Who can prove it? It's OK to say an idea

Hypothesis method
The assumption is wrong
Later, there was a contradiction in the calculation
So the hypothesis doesn't hold
It's over

1. The length of a rectangle is x cm and the circumference is 30 cm. If the length is reduced by 2 cm and the width is increased by 1 cm, then the rectangle becomes a square. From this, we can get the equation? (use the equation to solve)
2. The volume ratio of tank a, tank B and tank C is 7:8:9. Now there are 120 liters of oil in tank a, 190 liters of remaining oil in tank B and 210 liters of remaining oil in tank C. add 200 liters of oil into the three tanks respectively to make the three tanks just full. How much oil are the three tanks filled? (use equation solution)
3. There are two routes between a and B. someone rides along route one from a to B at the speed of 9 km / h, and then returns to a at the speed of 8 km / h along route two from B. It is known that route two is 2 km less than route one, and all the time is 8 / 1 hour less. Find the length of route one. (use equation solution)

1. The length of a rectangle is x cm, the circumference is 30 cm, then the width is 15-x cm. From the Title Meaning: X-2 = 15-x + 1. The solution is: x = 9 cm. 2. Suppose the volume of a, B and C tanks are 7x L, 8x L and 9x L respectively. Then: 7x + 8x + 9x = 120 + 190 + 210 + 200. The solution is: x = 30

One variable quadratic equation arithmetic problem
4X^2+2X-12=0.

4X²+2X-12=0
2x²+x-6=0
(2x-3)(x+2)=0
The solution is x = 2 / 3 or - 2

Is there any connection between junior three and junior two