In the right triangle ABC, the angle ABC is 90 degrees, the circle O with diameter AB intersects AC at e, and D is the midpoint on the side of BC, connecting de. it is proved that De is the tangent of circle o

In the right triangle ABC, the angle ABC is 90 degrees, the circle O with diameter AB intersects AC at e, and D is the midpoint on the side of BC, connecting de. it is proved that De is the tangent of circle o

Proof: connect OE, be
AB is the diameter, then ∠ AEB = 90 ° and ∠ BEC = 90 °; BD = CD, then de = BC / 2 = BD, ∠ DEB = ∠ DBE;
If ob = OE, then OEB = OBE
Therefore, OED = OBD = 90 degrees
So, De is the tangent of circle o

How can 1 2 3 = 4 be equal to 4

2-1+3=4

Zhangzhuang primary school used to have a rectangular playground, 50 meters long and 40 meters wide. When the campus was expanded, the length increased by 10 meters and the width increased by 8 meters. How many square meters has the playground increased?

(50 + 10) × (40 + 8) - 50 × 40 = 60 × 48-2000 = 2880-2000 = 880 square meters; a: the area of the playground has increased by 880 square meters

In the triangle ABC, if the three sides corresponding to angles a, B and C are a, B and C respectively, and they form an arithmetic sequence, the tolerance d > 0, and the maximum angle is twice the minimum angle, then a: B: C =?
Online. Thank you
Detailed steps should be taken

According to the meaning of the title, 2A = C, B = π - 3a, 2b = a + C sinA:sinB :sinC=a:b:c
The solution is: A: B: C = 4:5:6
first sinA:sinB=a : B B = π - 3A B = (a + C) / 2 SINB = sin3a = Sina [4 (COSA) ^ 2-1] to get 4 (COSA) ^ 2-1 = (a + C) / 2A (1)
again sinA:sinB=a : C sinc = sin2a = 2sinacosa, 2cosa = C / a (2)
Then square (2) and get the answer from (1) (2)

Given (x + my) (x + NY) = x2 + 2xy-8y2, find the value of m2N + Mn2

∵（x+my）（x+ny）=x2+2xy-8y2，∴x2+nxy+mxy+mny2=x2+（m+n）xy+mny2=x2+2xy-8y2，∴m+n=2，mn=-8，∴m2n+mn2=mn（m+n）=-8×2=-16．

Xiaohong's height is 150cm, 1 / 6 shorter than Xiaoming's. how many centimeters is Xiaoming's height

150 / (1-1 / 6) = 180, i.e. 180cm

In our life, we often use capillary phenomenon to solve problems, write four Liezi

Towel absorbent brick absorbent chalk absorbent ink towel absorbent sweat

Solution equation: 1.5x-x = 1

1.5X－X＝1
（1.5－1）X＝1
0.5X＝1
X＝1÷0.5
X＝2

A machine part is 10 mm long. How long does it take to draw it on paper at a scale of 50:1?

500 mm
That is to enlarge the parts by 50 times. What do I say about this process

Fill in the blanks in math,
The length of the three line segments are 3, X and | x-3 | + 2 respectively. Randomly select one of the five numbers 1, 2, 3, 4 and 5 as the value of X, which can make the probability of the three line segments forming an isosceles triangle equal to 0

It has been proved that x = 2,3,4 is isosceles triangle
So the probability is 3 / 5