Coordinate type: remember the solution of parabolic analytical formula (intersection point, vertex, etc.) ) and remember that the calculated line segment data should be transformed (for example, I found that OA=5, and he was in the second quadrant, so I changed it to A (-5,0).

Circle: The angles of the same arc (or equal arc) are equal, and the angles of the diameters on the circle are right angles. Many finale questions often need to add an auxiliary line, which has appeared frequently recently.

Triangle problem on the coordinate axis: either similar or pythagorean, absolutely!

Coordinates are tangent to the circle: two or more cases (classified discussion), such as tangent to the inside, tangent to the outside and tangent to the left and right, at least four cases.

The triangle is tangent to the circle: not only the inner tangent and the outer connection line should be considered, but also which side of the circle is tangent to the triangle. Generally speaking, a triangle has at least six tangent points, and each line has two (or so).

Moving point problem: the moving distance of a point = the length of the line segment where the point is located -xy (unknown moving time, y is the moving speed per second)-generally use similarity or pythagorean method to find x.

Maximum and minimum problem: the minimum value of a line segment is generally a vertical line segment, and the minimum value of n line segments is the vertical line segment from this line segment to each side.

Example: Three elves live in different places on the plane. Their walking speeds are 1 km, 2 km and 3km/h respectively. Where should we choose the meeting place to minimize the sum of the time they need to get to the meeting place from their residence (along a straight line)?

Answer: choose the elf residence with the walking speed of1km/h.

For convenience, the three fairies whose walking speeds are 1 km, 2 km and 3 km are called A, B and C respectively.

Let the distance between A and B be AB, and the distance between A and C be AC (please draw your own picture).

The total time to point A is T=AB/2+AC/3.

Suppose a certain point O is selected, and the distances from A, B and C to O are AO, BO and co(AO >；, respectively; 0)

a b-BO & lt； =AO，AC-CO & lt； =AO，

BO-AB & gt； =-AO，CO-AC & gt； =-AO

t=AO+BO/2+CO/3，

T-T = AO+(BO-AB)/2+(CO-AC)/3 & gt； = AO-AO/2-AO/3 = AO/6 & gt； 0

So AO>0, t>T

When AO=0, t is minimum.

Also choose the elf residence with the walking speed of per hour 1 km.

Then the rest depends on your ability to improvise. The data calculated in the last question will be a bit strange, but don't be discouraged. In the end, it will become just the right data (if not, it will basically be over, of course, a few possibilities will not be ruled out)