It is known that the distance between the cross sections of three points a, B, C and the center O of the sphere is equal to half of the radius of the sphere, and ab = BC = CA = 3

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• 1. If it is known that the cross sections of three points a, B and C on the sphere and the distance between the center of the sphere are equal to half of the radius of the sphere, and ab = BC = CA = 2, then the area of the sphere is?
• 2. There are three points a, B and C on the sphere. It is known that ab = 3, AC = 4 and BC = 5. If the distance from the center of the sphere to the plane ABC is 6, the surface area of the sphere is 0
• 3. If the length of two right sides of a right triangle is 3 and 4, and the distance from a point in the triangle to each side is equal, then the distance is______ ．
• 4. If the length of two right sides of a right triangle is 3 and 4, and the distance from a point in the triangle to each side is equal, then the distance is______ ．
• 5. As shown in the figure: in △ ABC, ab = AC, take a little E on AC, extend Ba to F, make AF = AE, and connect Fe. At this time, there is a special position relationship between Fe and BC. Can you find out and explain it?
• 6. In triangular pyramid p-abc, PA ⊥ plane ABC, AC ⊥ BC, through a as AE ⊥ PC, then PC to e, verification: AE ⊥ plane PBC
• 7. A mathematical problem: PA is known to be perpendicular to the plane where the circle O lies, AB is the diameter of the circle O, C is any point on the circle O, make AE through a, and make PC perpendicular to E A mathematical problem: we know the plane where PA is perpendicular to circle O, AB is the diameter of circle O, C is any point on circle O, make AE perpendicular to PC through a, and prove that AE is perpendicular to plane PBC
• 8. It is known that PA is perpendicular to the plane of circle O, AB is the diameter of circle O, C is any point on circle O, and AE is perpendicular to PC through a Results: AE was perpendicular to the plane of PBC
• 9. AB is the diameter of circle O, C is the point on circle O, PA is perpendicular to the plane of circle O, AE is perpendicular to Pb is perpendicular to e, AF is perpendicular to PC is perpendicular to F Let PA = root 3 and AC = 1 to find the distance between point a and PCB
• 10. In the regular triangular pyramid p-abc, e f is the midpoint of the side edges Pb and BC respectively, and AE ⊥ EF, PA = root 2 to calculate the volume
• 11. It is known that the distance from the cross section of three points a, B and C on the sphere to the center of the sphere is equal to half of the radius of the sphere, and AC = BC = 6, ab = 4. The surface area and volume of the sphere are calculated
• 12. It is known that the distance from the cross section of three points a, B and C on the sphere to the center O is equal to half of the radius, and ab = BC = CA = 3cm I want the most clear and easy to understand answer process
• 13. ABC is an equilateral triangle with side length 4. If the distance between a, B, C and plane a is the root sign 3, how many are there?
• 14. In the plane of the triangle ABC, how many points are equidistant from the three sides of the triangle ABC?
• 15. Track: the number of points on the plane of triangle ABC, which is equal to the distance between the three sides of the straight line, is____ One
• 16. Let p be a point outside the plane where △ ABC lies, the distance between P and a, B, C is equal, and ∠ BAC is a right angle
• 17. Let a (2,3,1) B (4,1,2) C (6,3,7) d (- 5, - 4,8) find the distance from D to plane ABC, Let a (2,3,1) B (4,1,2) C (6,3,7) d (- 5, - 4,8) find the distance from D to plane ABC?
• 18. Given a (2,3,1) B (4,1,2) C (6,3,7) d (- 5, - 4,8), find the distance from D to plane ABC
• 19. Let a (2,3,1), B (4,1,2), C (6,3,7), D (- 5, - 4,8), then the distance from D to plane ABC is?
• 20. In space, it is shared with the plane whose distance from the three vertices of △ ABC is 1cm______ ．