There is a square ABCD whose side length is Q. P is a point on the diagonal BD. when p is at what position, the value of AP + BP + CP is the minimum

The minimum value is not 3 / 2 √ 2q, because we can find a smaller value: when P and B coincide, AP + BP + CP = 2q. To find the minimum value of L = AP + BP + CP, we can use the method of analytic geometry

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1. It is known that square ABCD is inscribed at O, and point P is a point on inferior arc ad. it connects AP, BP, CP and (AP + CP) / BP (important process)
2. P is a moving point outside the rectangular ABCD, and satisfies the AP vertical CP BP.DP When point P changes, does the degree of angle BPD change? If not, calculate the degree of angle BPD; if not, calculate the range of change
3. As shown in the figure, in square ABCD, points E and F are on edge BC and CD respectively. If AE = 4, EF = 3 and AF = 5, then the area of square ABCD is equal to () A. 22516B. 25615C. 25617D. 28916
4. As shown in the figure, in square ABCD, points E and F are on edge BC and CD respectively. If AE = 4, EF = 3 and AF = 5, then the area of square ABCD is equal to () A. 22516B. 25615C. 25617D. 28916
5. ABCD is a square, AE = 4, EF = 3, AF = 5, find the area of ABCD E is on BC, f is on CD
6. As shown in the figure, in square ABCD, points E and F are on edge BC and CD respectively. If AE = 4, EF = 3 and AF = 5, then the area of square ABCD is equal to () A. 22516B. 25615C. 25617D. 28916
7. As shown in the figure, in square ABCD, points E and F are on edge BC and CD respectively. If AE = 4, EF = 3 and AF = 5, then the area of square ABCD is equal to () A. 22516B. 25615C. 25617D. 28916
8. The vertex a of the square ABCD is in the shape ∠ EAF = 45 °, e, f is in the shape BC.CD Let EF be ah ⊥ EF in H. prove ah = ab
9. As shown in the figure, EF is the two points AE parallel CF on the diagonal BD of the quadrilateral ABCD, AE = CF, be = DF to prove the congruent triangle CBF of the triangle ade
10. In a pyramid p-abcd, planar pad ⊥ planar ABCD, ab ∥ CD, △ pad are equilateral triangles. It is known that BD = 2ad = 8, ab = 2dc = 4 √ 5 Let m be a point on PC, and prove that planar MBD ⊥ planar pad
11. There is a point in rectangle ABCD, P AP = 8 bp = 7 CP = 6 DP =?
12. In rectangular ABCD, there is a point P, AP = 3, DP = 4, CP = 5, BP =? How to calculate?
13. In rectangle ABCD, take any point P, connect AP, BP, CP, DP, ask the relationship of AP, BP, CP, DP
14. Point P is a point in the square ABCD, connecting AP, BP, CP, DP. If △ ABP is an equilateral triangle, find the degree of ∠ cpd
15. In the pyramid p-abcd, the bottom surface ABCD is a distance shape, PA ⊥ ABCD, the point E is on PC, and the PC ⊥ surface BDE In the pyramid p-abcd, the bottom surface ABCD is a distance shape, PA ⊥ ABCD, the point E is on PC, and the PC ⊥ surface BDE is: ① prove: the BD ⊥ surface PAC; ② if PA = 1, ad = 2, find: the tangent value of the face angle b-pc-a
16. The diamond ABCD is on the plane a, PA is perpendicular to a, and PC is perpendicular to BD
17. As shown in the figure, the quadrilateral ABCD is a square, PD ⊥ plane ABCD, EC ∥ PD, and PD = 2ec. (I) prove: plane PBE ⊥ plane PBD; (II) if the dihedral angle p-ab-d is 45 °, find the sine value of the angle between the straight line PA and the plane PBE
18. The triangle ABCD is a square, PD ⊥ face ABCD, PD = PC, e is the midpoint of PC,
19. The edge length of cube abcd-a'b'c'd 'is 1. Find the distance from point C to plane c'bd
20. In the cube abcd-a1b1c1d1 with edge length 1, (1) find the distance from point a to plane BD1; (2) find the distance from point A1 to plane ab1d1; (3) find the distance between plane ab1d1 and plane BC1D; (4) find the distance from line AB to cda1b1