, .
, . .
- , . .
- , , , 180 . . 180 .
, , . , .
.
A(m;-3) B(1;5) 10. m.
.
. sqrt(), , .
.
sqrt((x1-x2)2+(y1-y2)2 ),
sqrt((m-1)2+(-3-5)2),
, 10,
sqrt((m-1)2+(-3-5)2) = 10
(m-1)2+(-3-5)2 = 100
m2- 2m + 65 = 100
m2- 2m - 35 = 0
D = 144
x1=7
x2=-5
: m 7 -5
.
, y A(-2;3) B(6;1).
.
. sqrt(), , .
. , , . , BC AC.
BC = AC
.
sqrt((x1-x2)2+(y1-y2)2 ),
, , y, x=0.
AC = sqrt((-2 - 0)2 +(3 - y)2)
BC = sqrt((0 - 6)2 +(y - 1)2)
AC=BC,
sqrt((-2 - 0)2 +(3 - y)2) = sqrt((0 - 6)2 +(y - 1)2)
(-2 - 0)2 +(3 - y)2 = (0 - 6)2 +(y - 1)2
4 + 9 - 6y + y2 = 36 + y2 - 2y + 1
- 6y + 2y + y2- y2 =36 + 1 - 4 - 9
- 4y = 24
y = -6
: (0;-6)
.
, A(-2;-3), B(2;1) C(7;6) . ?
.
, (x1;y1) (x2;y2)
(y - y1) / (y2 - y1) = (x - x1) / (x2-x1)
AB. A(-2;-3), B(2;1). :
|
|
(y - (-3)) / (1 - (-3)) = (x - (-2)) / (2 - (-2))
(y + 3) / 4 = (x + 2) / 4
y + 3 = x + 2
y = x - 1
, , . , , :
y = 7 - 1 = 6
C(7;6)
: A, B, C
. ( ). , - . " " sqrt(), sqrt - , .
.
ABC, A(-3;2), B(5;3), C(-4;-3). .
.
,
|a1b1+a2b2| / (sqrt(a1+a2) + sqrt(b1+b2))
:
cos AB = -(-3*5 + 2 * 3) / (√13 √34) ≈ 0.428
cos BC = -(5*(-4) + 3 * (-3)) / (5 √34) ≈ 0.995
cos AC = -(-3*(-4) + 2 * (-3)) / (5 √13) ≈ -0.333
64,7, 5,7 109,6
. .
.
, , 40 . . | , , 40 . . |
.
AD BC O, AOC 40 .
AOC BOD - , , , . ∠AOC = ∠BOD = 40
AOC DOC - . , 180 .
, ∠AOC + ∠DOC = 180 ,
∠DOC = 180 - 40 = 120
DOC AOD - , , ∠DOC = ∠AOD = 120
: , 40, 120, 40 120 .
. . , - . .
.
, 107
.
C, D.
C - D = 107
= 2πR = πD,
πD - D = 107
D (π - 1) = 107
D = 107 / (π - 1) ≈ 49,96
R = D / 2 = 107 / 2(π - 1) ≈ 24,98
: 107 / 2(π - 1) ≈ 24,98
.
, , - , m. .
.
,
r = √3/6 a
,
R = √3/3 a
|
|
R - r = m,
√3/3 a - √3/6 a = m
a (√3/3 - √3/6) = m
a √3/6 = m
a = 6m / √3
: 6m / √3
. , .
.
D S, AS:SB = 2:3, DS = 12, SC = 5, .
.
AS:SB = 2:3, AS = 2x, SB = 3x
AS x SB = CS x SD,
2 * 3 = 5 * 12
62 = 60
2 = 10
x = √10
AB = AS + SB
AB = 2√10 + 3√10= 5√10
: 5√10
.
, 3,5:5,5:3 . .
.
, . . , , ().
360 ,
3,5 + 5,5 + 3 = 360
12 = 360
= 30
:
3 * 30 = 90
3,5 *30 = 105
5,5 *30 = 165
, . , .
:
90 / 2 = 45
105 / 2 = 52,5
165 / 2 = 82,5
: 45; 52,5; 82,5;
. , . .
.
ABC ( C = 900) CD. CD, AD = 9 , BD = 16
.
ABC, ACD CBD . ( ).
- , , .
: ABC, ACD, CBD. . ( A ABC A ACD C CBD . .)
ABC CBD . :
AD/DC = DC/BD,
DC2=AD*BD
DC2=9*16
DC=12