As shown in the figure, point B is on line ad, C is the midpoint of line BD, ad = 10, BC = 3. Find the length of line CD and ab

As shown in the figure, point B is on line ad, C is the midpoint of line BD, ad = 10, BC = 3. Find the length of line CD and ab

∵ C is the midpoint of the line BD, ∵ BC = CD, ∵ BC = 3, ∵ CD = 3; from the graph, ab = ad-bc-cd, ∵ ad = 10, BC = 3, ∵ AB = 10-3-3 = 4

A. B, C, D are the four points in order on the straight line AB: BC = BC: CD = 1:2, e, f are the midpoint of AB, CD, EF = 13.5cm, find the length of line ad

Because AB: BC: CD = 1:2:4 = 2:4:8
So, ad: EF = ad: 13.5 = (2 + 4 + 8): (1 + 4 + 4)
AD=21

If a line segment is sandwiched in two half planes of a straight dihedral angle and its angles to the two half planes are 30 degrees, then the angle between the line segment and the edge of the dihedral angle is 30 degrees___ ．

As shown in the figure, the two ends of AB, a ∈ α, B ∈ β, pass through a point to make AA ′⊥ β, intersect β at a ′, connect BA ′, then ∠ ABA ′ is the angle between AB and β, and ∠ ABA ′ = 30 °, similarly, pass through B to make BB ′⊥ α, intersect α at B ′, then ∠ bab ′ is the angle between BB ′ and α, and ∠ bab ′ = 30 °. Pass B to make BD ‖ a ′ B ′ and BD = a ′ B ', then ∠ abd is the calculated a ′ B ′ and BD is a parallelogram In the right angle △ ABB ', BB ′ = absin30 ° = AB2 in the right angle △ ABA', AA ′ = absin30 ° = AB2, a ′ B = abcos30 ° = 3ab2 in the right angle △ a ′ BD, BD = 22a ′ B in the right angle △ abd, sin ∠ abd = ADAB = 22,  abd = 45 degree, so the answer is: 45 degree

If a line segment is sandwiched in two half planes of a straight dihedral angle and its angles to the two half planes are 30 degrees, then the angle between the line segment and the edge of the dihedral angle is 30 degrees___ ．

As shown in the figure, the two ends of AB, a ∈ α, B ∈ β, pass through a point to make AA ′⊥ β, intersect β at a ′, connect BA ′, then ∠ ABA ′ is the angle between AB and β, and ∠ ABA ′ = 30 °, similarly, pass through B to make BB ′⊥ α, intersect α at B ′, then ∠ bab ′ is the angle between BB ′ and α, and ∠ bab ′ = 30 °

As shown in the figure, plane a ⊥ plane β, a ∩ β = L, a ∈ β, B ∈ a, and the angle between AB and l is 60 degrees, the distance between a and B to L is 1 and the root is 3 respectively, then the distance between a and B to L is calculated

Make ad ⊥ L in D in plane β, CD ⊥ L in plane α, BC ⊥ CD in C, connect AC
Then ad = 1
CD=√3
∴AC=2
The angle between AB and l is 60 degrees
∴∠ABC=60°
∴AB=4√3/3
(I'll save the proof process)

As shown in the figure, the line segment AB is in plane a, the line segment AC is perpendicular to a, the line segment BD is perpendicular to AB, and ab = 7, AC = BD = 24, CD = 25?

Let the midpoint of AC be f
∵AB⊥BD、AB＝7、BD＝24,∴AD＝√（AB^2＋BD^2）＝√（49＋576）＝√625＝25,
CD = 25, ad = CD, AF = CF = AC / 2 = 12, FD ⊥ AC
∵ AC ⊥ plane α, de ⊥ plane α, ∥ FA ∥ De
∵ AC ⊥ plane α, ∵ AE ⊥ AC, combined with the proved FD ⊥ AC, we get: FD ∥ AE
From FA ∥ de and FD ∥ AE, it is concluded that AEDF is a parallelogram, and ∥ de = AF = 12
∴sin∠DBE＝DE/BD＝12/24＝1/2,∴∠DBE＝30°.
The angle between BD and plane α is 30 degrees

There are two points a and B on the edge of the dihedral angle of 120 & #, AC and BD are the line segments perpendicular to AB in α and β respectively, ab = 2, AC = 3 and BD = 4 are known, and CD is calculated

Make be ⊥ AB in the plane α, and take the line segment be = AC to connect CE and de. because BD ⊥ AB and BD are in the plane β, we can see that: ⊥ DBE is the plane angle of dihedral angle c-ab-d. then: ⊥ DBE = 120 ° and there is ab ⊥ plane BDE. Because AC ⊥ AB, be ⊥ AB, be and AC are in the plane α, so: AC / / be and be = AC, so

Given the dihedral angle α - L - β, the point a ∈ α, AC ⊥ L, C is perpendicular, the point B ∈ β, BD ⊥ L, D is perpendicular. If AB = 2, AC = BD = 1, then CD=______ ．

Connect BC, ∨ AC ⊥ L, α ⊥ β, α ∩ β = L, ∩ AC ⊥ β, BC ⊂ β, ⊂ AC ⊥ BC, similarly BD ⊥ α, CD ⊂ α, BD ⊥ CD, let CD = x, BC2 = 12 + X2, AB2 = BC2 + ac2 = 1 + 1 + x2 = 4, ⊂ x = 2, so the answer is 2

If the radii of the two circles are 3 and 4 respectively, and the center distance is 7, then the position relationship between the two circles is ()
A. Disjoint B. circumscribe C. inscribe D. intersect

∵ the radii of the two circles are 3 and 4 respectively, the center distance of the circle is 7, ∵ 3 + 4 = 7, ∵ the position relationship of the two circles is circumscribed, so B is selected

It is known that the radii of the two circles are 3 and 4 respectively, and the center distance D satisfies D square-8d + 7

D square - 8D + 7