In △ ABC. Ab ⊥ AC, ad ⊥ BC in D, the proof: 1 / ad ^ 2 = 1 / AB ^ 2 + 1 / AC ^ 2 So in the tetrahedral ABCD, what kind of conjecture can you get by analogy with the above conclusion, and explain the reason

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• 1. It is known that plane α and β satisfy α⊥ β, α∩ β = L, straight line AB is in plane α, ab ⊥ L, straight line BC and de are in plane β, and BC ⊥ de. the proof is AC ⊥ De
• 2. Given △ ABC, linear L ⊥ AB, l ⊥ AC, prove L ⊥ BC
• 3. In the triangle ABC, BC = a, AB + AC = L, make a vertical line from the bisector of the outer angle a 'of the angles B and C, and prove that BD * AE = fixed value with the perpendicular feet of D and E
• 4. It is known that a + B + C = 2,0
• 5. Given a + B + C = 0, AB + BC + AC = 0, prove a = b = C = 0
• 6. Prove that a ^ 2 + B ^ 2 + C ^ 2-ab-ac-bc is a nonnegative number
• 7. If we know the square of a + the square of B + the square of C - AB BC AC = 0, we can judge the size relation of ABC quickly
• 8. In △ ABC, ∠ ABC = 90 degrees, D, E on AB, ad = AC, be = BC, try to judge whether the size of ∠ DCE is related to the size of ∠ B, if so, ask for the relationship between them, determine the degree, and explain the reason wait anxiously A |\E | D C -----------B Can't upload graphics, so that means. I hope I can understand it. A. B and C are △ and there are lines from e to C and D to C respectively.
• 9. Given a & # 178; + B & # 178; + C & # 178; = AB + AC + BC, judge the relationship between a, B and C
• 10. Given that the lengths of three sides of a triangle a, B, C satisfy a & # 178; + B & # 178; + C & # 178; - AB BC AC = 0, try to judge the shape of the triangle
• 11. Given a + B + C = 0, prove AB + BC + AC = 1
• 12. There is a mathematical problem: a natural number a, a total of 10 divisors, including 1 and a, to find the product of these divisors
• 13. The natural number n has 45 positive divisors. The minimum value of n is______ ．
• 14. How many positive divisors does 75600 have? How many odd divisors? Point out the ideas, thank you!
• 15. The divisor of 120, All divisors of 120 (except 1) are written as the product of prime factors of 120
• 16. Is there a point Q on the positive half axis of the x-axis for the motion of the moving point P on the ellipse with the equation x ^ 2 / 9 + y ^ 2 / 4 = 1, so that the shortest distance between the point on the trajectory equation of Q and P is 1? If there is, find the Q coordinate. If not, explain the reason
• 17. 1. The A.B.C of the ellipse is known to be an equal ratio sequence, and the eccentricity is calculated 2. If the endpoint of the minor axis of the ellipse and the two focal points form an isosceles right triangle, calculate the eccentricity
• 18. On ellipses The coordinates of two fixed points a and B of triangle ABC are respectively - 6060. The product of the slope of the straight line where AC BC is located is equal to - 9 / 4. Find the trajectory equation of fixed point C
• 19. It is known that the center of the ellipse is at the origin and the focus is on the x-axis. The area of the quadrilateral obtained by connecting its four vertices is 42. Connect a point on the ellipse (except the vertex) and the four vertices of the ellipse respectively. The product of the slopes of the four straight lines where the line segment is located is 14. The standard equation of the ellipse is obtained
• 20. 2 times (a quadratic + B quadratic + C quadratic) > a quadratic (B + C) + B quadratic (a + C) + C quadratic (a + b) Here's a picture of you. You can see it more clearly