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18.03.2013

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SΔ = ½ aha, ha - ;

SΔ = ½ ab sin ∠C;

SΔ = p(p - a)(p - b)(p - c), p - , p = ½ (a + b + c);

SΔ = pr, r - , ;

SΔ = abc/4R, R - , .


.

c2 = a2 + b2;

hc2 = |AD||DB|;

b2 = |AB||AD|;

a2 = |AB||BD|;


.

SΔ = ¼ a23;

a = R3, R - , ;

a = 2r3, r - , .


.

|AF| = ha - , |AE| = na - , |AD| = ma - ABC, A. R - , . r - , ;

|AB|:|AC| = |BE|:|EC|;

ha = ½ bc/R;

ha = 2p(p - a)(p - b)(p - c)/a, p - ;

na = bc(a + b + c)(b + c - a)/(b + c);

ma = ½ 2b2 + 2c2 - a2;

2:1, ;


.

α - , β - , α = β180/π, β = απ/180;

C = 2πr, C - .

S = πr2;

l = πrα/180 = rβ, l - AKB;

SOAKB = ½ r2β = πr2α/360, SOAKB - OAKB;
    SAKB = ½ r2(απ/180 - sin α) = ½ r2(β - sin β), SAKB AKB.


.

S = bh, h - ;

S = absin ∠A;

S = ½ |AC||BD| sin α;

2(a2 + b2) = |AC|2 + |BD|2.


.

S = ½ |AC||BD|;

S = |AD|h;

S = a2 sin ∠A.


.

|KE| = ½ (|BC| + |AD|), KE - AB BD;

S = |KE|h;

S = ½ (|BC| + |AD|)h.


n-.

Sn = ½ Pnr, Pn - n-;

Sn = ¼ na2 : tg 180/n;

Sn = nr2tg 180/n;

Sn = ½ nR2sin 360/n;

a = 2rtg 180/n;

a = 2Rsin 180/n;


s n-.

n- 180(n - 2).


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