Multi-solution type circle
1, and the maximum and minimum distances from a point to a circle on the plane are 6 and 2, respectively. Find the diameter of a circle. (When the point is inside or outside the circle, the diameter is 6+2 or 6-2. )
2. The lengths of two chords of a circle are 6 and 8, and the radius is 5. Find the distance between two chords. (When the chords are on the same side and both sides of the center, the distance is 4+3 or 4-3. )
3. In a circle with a radius of 4, what is the circumferential angle of a chord with a length of 4? (The circumferential angle of the upper arc and the lower arc is 30 or150. )
4. The radii of two tangent circles are 4 and 6 respectively. Find the center distance. (In both cases, the center distance is 6-4 or 6+4).
5. The radii of the two intersecting circles are 25 and 39 respectively, and the chord length is 30. Find the center distance. (When the two centers are on the same side and on both sides of the chord, it is 36-20 or 36+20. )
6. The radius of the circumscribed circle of triangle ABC is 4, and BC=4. Find the degree of angle A.. (When the center of the circle is inside and outside the triangle, it is 30 degrees or 150 degrees. )
Second, the multiple problem-solving types of numbers.
1, the inverse of a is itself, and the reciprocal of b is itself. What is the value of a-b? (The reciprocal itself is a number of 1 and-1, and the result is-1 or 1).
2. Its square itself is a number of _ _ _ _ (0 or 1).
The cube root of a is 2. What is the square root of a? A positive number has two square roots, which are plus or minus 2. )
4. The squares of A and B are equal, a+2=3, what's the difference between b-2? (Square-equal numbers are either equal or opposite, b is 1 or-1, and the difference is-1 or -3).
5. What is the sum of a number with an absolute value of 5 and a number with a square root of 3? (There are two numbers whose absolute values are positive and the sum is 8 or -2)
6. On the number axis, what is the reciprocal of 1.5 when the distance from the point representing 2 is equal to 6? (The number represented by a point with a distance of 6 is the original number plus or minus 6, and the result is -6 times or 12 times. )
How to solve this problem?
In the rectangular ABCD, AB=3, AD= 1, and point p moves on line segment AB. Let AP = X. Now fold the paper so that point D coincides with point P to get the crease EF (point E and point F are the intersection of the crease and the rectangular edge), and then restore the paper.
(1) Please write the range of X that makes the quadrilateral EPFD a diamond, and find the side length of the diamond when X=2;
(2) Let the square of EF be equal to Y. When point E is in AD and point F is in BC, write the functional relationship between Y and X. When y takes the maximum value, do you judge whether △EAP and △PBF are similar? Give reasons