As shown in the figure, it is known that in isosceles △ ABC, the vertex angle ∠ a = 36 ° and BD is the bisector of ∠ ABC The value of AC is equal to () A. 1 Two B. 5−1 Two C. 1 D. 5+1 Two

As shown in the figure, it is known that in isosceles △ ABC, the vertex angle ∠ a = 36 ° and BD is the bisector of ∠ ABC The value of AC is equal to () A. 1 Two B. 5−1 Two C. 1 D. 5+1 Two

∵ isosceles ᙽ ABC, vertex angle ∠ a = 36 °
∴∠ABC=72°
And ∵ BD is the angular bisector of ∵ ABC
∴∠ABD=∠DBC=36°=∠A
And ∵ C = ∵ C
∴△ABC∽△BDC
∴CD
BC＝BC
AB
Let ad = x, ab = y,
∵∠A=∠ABD，∴BD=AD，
Then BC = BD = ad = x, CD = y-x
∴y−x
x＝x
y. Suppose X
If y = k, then the above equation can be changed to 1
k-1=k
The solution is: K=
5−1
2, then ad
The value of AC is equal to
5−1
2．
Therefore, B

In the isosceles triangle ABC, if the vertex angle a is equal to 36 ° and BD is the bisector of angle ABC, what is the value of ad to AC

Draw your own picture: the angle ABC = 72 ° after bisection, abd and DBC are 36 ° respectively
The triangle abd and the triangle BDC are isosceles triangles. There is ad = BD = BC
It is proved that triangle ABC is similar to triangle BDC
AD:AC=BC:AC=DC:BC=DC:AD
Ad ^ 2 = DC * AC
AD^2=AC(AC-AD)
AD^2-AC^2+AC*AD=0
Ad: AC = - 1 / 2 ±√ 3 / 2 where ad: AC = - 1 / 2 - √ 3 / 2 (omitted)
So ad: AC = √ 3 / 2-1 / 2

In the isosceles triangle ABC, the top angle ∠ a = 36 degrees, and the bisector BD of the base angle intersects AC with D. D is the golden section point of the line AC. if AC = 10 cm, find the length of AD

AD=10*0.618=6.18 cm
Analysis: the key is to look at the size of CD and ad, we can know who is the big side of golden section
Because AB = AC, ∠ a = 36 degrees
So ∠ ABC = ∠ BCD = 72 degrees
Therefore, abd = CBD = 36 degrees
So ad = BD
Because ∠ CBD ＜∠ BCD, from the big angle to the big side
So CD

As shown in the figure, it is known that in isosceles △ ABC, the vertex angle ∠ a = 36 ° and BD is the bisector of ∠ ABC The value of AC is equal to () A. 1 Two B. 5−1 Two C. 1 D. 5+1 Two

∵ isosceles ᙽ ABC, vertex angle ∠ a = 36 °
∴∠ABC=72°
And ∵ BD is the angular bisector of ∵ ABC
∴∠ABD=∠DBC=36°=∠A
And ∵ C = ∵ C
∴△ABC∽△BDC
∴CD
BC＝BC
AB
Let ad = x, ab = y,
∵∠A=∠ABD，∴BD=AD，
Then BC = BD = ad = x, CD = y-x
∴y−x
x＝x
y. Suppose X
If y = k, then the above equation can be changed to 1
k-1=k
The solution is: K=
5−1
2, then ad
The value of AC is equal to
5−1
2．
Therefore, B

If the radius of the bottom of the cone is 1cm and the length of the generatrix is 3cm, the total area of the cone is () cm2 A. π B. 3π C. 4π D. 7π

The circumference of the bottom surface of the cone is 2 π × 1 = 2 π,
So the side area of the cone is 1
2×2π×3=3π，
The base area of the cone is π × 12 = π,
So the total area of the cone is 3 π + π = 4 π (cm 2)
Therefore, C

If the radius of the bottom of the cone is 1cm and the length of the generatrix is 3cm, the total area of the cone is () cm2 A. π B. 3π C. 4π D. 7π

The circumference of the bottom surface of the cone is 2 π × 1 = 2 π,
So the side area of the cone is 1
2×2π×3=3π，
The base area of the cone is π × 12 = π,
So the total area of the cone is 3 π + π = 4 π (cm 2)
Therefore, C

If the radius of the bottom area of the cone is 1 cm and the length of the bus bar is 3 cm, then the area of the cone is?

Base area = π R ^ 2 = π * 1 ^ 2 = π square centimeter
Side area = (1 / 2) bottom perimeter * bus length = (1 / 2) * 2 π R * 3 = 3 π cm2
Total area = ground area + side area = π + 3 π = 4 π square centimeter

The section of a conical part passing through the shaft is an isosceles triangle whose waist length is equal to the ground diameter of the cone, and the height of the cone is twice as many as three conic generatrix

The section of a conical part passing through the shaft is an isosceles triangle, and because the waist length is equal to the diameter of the bottom surface of the cone, the section is an equilateral triangle, and the conical generatrix L = waist length = bottom diameter. Therefore, the bottom diameter / 2 = generatrix L / 2, l? = height? + (bottom diameter / 2) YL? = (2 √ 3) mm2 +

The section of a generatrix parallel to a cone is an isosceles triangle The following statement is correct () A. The section of a generatrix parallel to the cone is an isosceles triangle B. The section of a generatrix parallel to the cone is isosceles trapezoid C. The section passing through the apex of a cone is an isosceles triangle D. The cross section passing through the center of the bottom surface of the cone is isosceles trapezoid

C

The axial section of the cone is an isosceles triangle with the diameter of the bottom surface of the cone as the bottom edge and the generatrix of the cone as the waist. If the diameter of the bottom surface of the cone BC = 4 cm and the generatrix AB = 6 cm, the shortest distance from the point to the generatrix is [] Why triple and triple

Because the diameter of the bottom circle is ab = 4
So the perimeter of the bottom is equal to 4 PI
Development angle = 360r / L = 360 * 2 / 6 = 120 degrees
So ∠ APB = 0.5 ∠ APA '= 60 degrees
So ∠ PAA '= 30 degrees
Pythagorean root (6-3) = 3