In RT △ ABC, AC = 3, BC = 4, ab = 5, point P is any point on the inscribed circle of △ ABC, find | PA | ^ 2 + | Pb | ^ 2 + | PC | ^ 2 Minimum value of It should be done with the parametric equation of the circle | Math enthusiast | Mathematical art

In RT △ ABC, AC = 3, BC = 4, ab = 5, point P is any point on the inscribed circle of △ ABC, find | PA | ^ 2 + | Pb | ^ 2 + | PC | ^ 2 Minimum value of It should be done with the parametric equation of the circle

Establish a rectangular coordinate system (two methods, I choose one) C as the origin, CA is the positive direction of X axis, CB is the positive direction of Y axis, C (0,0) a (3,0) B (0,4) inscribed circle radius is calculated first, r = area divided by half perimeter = 6 / 6 = 1, so the equation of circle center (1,1) radius 1 is (x-1) &# 178; + (Y-1) &# 178; = 1 parameter equation x =

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1. Let a = {a │ a = 2x3y5z, x, y, Z, ∈ n} (2x is the x power of 2), and B = {B │ B ∈ a, 1 ≤ B ≤ 10}. Then, we find the sum of subsets containing elements 1 and 10 in set B Find the number of subsets. Please explain the reason
2. As shown in the figure, in isosceles trapezoid ABCD, ∠ C = 60 ° ad = CD, e and F are on AD and CD respectively, de = CF, AF and be intersect at p. find the size of ∠ BPF
3. A limit, its odd limit and even limit are equal to 1. Why is its limit equal to 1 instead of 2? Please answer in detail
4. As shown in the figure, in △ ABC, the vertical bisector of BC intersects AB at point E. if the perimeter of △ ABC is 10 and BC = 4, then the perimeter of △ ace is______ ．
5. Why is it not necessary to follow the parallelogram rule when calculating the work of resultant force?
6. 1-178; + 2-178; + 3-178; + 4-178; + 25-178; = 5525 2²+4²+6²+8².+50²=【】
7. The central symmetry formula and symmetry axis formula of mathematics function in senior one compulsory 4 The central symmetry formula of Sin & nbsp; Cos & nbsp; Tan and the formula of symmetry axis should be & nbsp;
8. Given the function f (x) = X3 + AX2 + BX + C (where a, B, C are constants), if y = f (x) obtains the maximum and minimum values respectively when x = - 1 and x = - 13, then a=______ ．
9. We make to show card how a
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12. Direct triangle, three sides are arithmetic sequence, known area is 12. Find perimeter
13. Cosine value of a / 2 + C = 4 / 5, area of triangle ABC = vector AB * vector BC, find cosine value of A Who will help solve the problem of grade one in senior high school!
14. As shown in the figure, △ ABC is an equilateral triangle, and points D, e and F are points on line AB, BC and Ca respectively. (1) if ad = be = CF, is △ def an equilateral triangle? (2) if △ DEF is an equilateral triangle, is ad = be = CF true? Try to prove your conclusion
15. For example, if I give the coordinates of two vectors a and B, how can I find a · B? Can I directly multiply them by coordinates?
16. As shown in the figure, AE ⊥ CE in E, EB ⊥ AC in B, BD ⊥ AE in D, try to compare the size of AB, AC, ad, AE?
17. On the cosine value of the angle between line and plane in space by vector For the problem of the angle between a line and a plane in space, can we first find the normal vector of a line, then find the normal vector of a surface, and then find the angle between two normal vectors, and then find the cosine of the angle complementary to the angle? Or do we first find the normal vector of the surface, and then find the angle between the normal vector and the line vector?
18. As shown in the figure, △ ABC, D and E are the midpoint of BC and AC respectively. BF bisects ∠ ABC and intersects de at point F. if BC = 6, the length of DF is______ ．
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20. A circle is an axisymmetric figure, and each axis is its axis Is that right or wrong?