Тема 4. Геометрические задачи

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1. M (2; -1; 4) 2. B (-10; 3; 1) 3. A (2; -3; 0) 4. M (2; -4; 3) 5. B (-2; 6; -1) 6. A (-8; -4; -11)

7. M (1; -2; 6) 8. B (6; -13; -2) 9. A (2; 4; -7) 10. M (3; -2; 4) 11. B (10; -7; -13) 12. A (-7; 7; -6)

1. = , a = , b = c = , A = , B = C =

2. = 42 , a = 5 , b = 17, c = 13, A = arccos , B =  - arccos , C =

3. = , a = , b = c = 3, A =  - arccos , B = C = arccos

4. = , a = b = c = , A = B = C =

5. = , a = , b = 3, c = , A = , B = arccos C = arccos

6. = , a = 6 , b = 3, c = 13, A = arccos , B = arccos , C =  - arccos

7. = 7 , a = 2 , b = 17, c = 3, A = arccos , B =  - arccos , C = arccos

8. = 5 , a = 3 , b = 2, c = 25, A = arccos , B = arccos , C =  - arccos

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1. V = 34; S = 14; H = 7 2. V = 18; S = 14; H = 4 3. V = 83; S = 25; H = 5

4. V =12; S = 6; H =2 5. V =11; S =; H = 6. V = 12; S = 3; H =

7. V = 26; S = 8; H = 8. V =23; S =; H =2



1. О(- ; 4); S = 24; a = 3 b = 10 c = 5; r = 2(5 - )  1,75 R =  6,44

A =  - arccos  106,26 B = arccos  50,91 C = arccos  22,83;

m_A = m_B = 8 m_C = ; h_A = h_B = 4 h_C = 9 ; M (-2;5) l_A = = 4

2. О(-1 ; -2); S = 25; a = 5 b = 10 c = 5; r =  1,91 R =  5,59

A = 90 B = arccos  63,43 C = arccos  26,57;

m_A = m_B = 5 m_C = ; h_A = 2 h_B = 5 h_C = 10; M (-2 ; -3 ) l_A = =

3. О(5 ; - ); S = 28; a = 2 b = 13 c = 5; r =  1,64 R =  9,36

A =  - arccos  120,51 B = arccos  44 C = arccos  15,49;

m_A = 4 m_B = m_C = ; h_A = h_B = 4 h_C = 11; M (6 ; 1) l_A = =

4. О(1; -1); S = 63; a = 3 b = 13 c = 10; r =  3,05 R =  9,41

A =  - arccos  104,25 B = arccos  43,67 C = arccos  32,08;

m_A = m_B = m_C = ; h_A = h_B = 9 h_C = 12 ; M (3 ; - ) l_A = =

5. О(-2 ; 7); S = 16; a = 13 b = c = 10; r =  1,18 R =  8,38

A =  - arccos  129,09 B = arccos  14,25 C = arccos  36,66;

m_A = m_B = m_C = 2; h_A = 2 h_B = h_C = 3; M (; 5) l_B = =

6. О(-2 ; -2); S = 7; a = 5 b = c = 10; r =  0,69 R =  9,62

A = arccos  15,07 B = arccos  16,26 C =  - arccos  148,67;

m_A = m_B = m_C = ; h_A = 2 h_B = h_C = 1 ; M (-1; -1) l_B = =

7. О(8; 1); S = 24; a = 5 b = c = 10; r =  1,93 R =  5,13

A = arccos  29,17 B = arccos  73,74 C = arccos  77,09;

m_A = m_B = m_C = 6; h_A = 9 h_B = h_C = 4 ; M (9; - ) l_B = = 5

8. О(-1 ; -1); S = 33; a = 13 b = 3 c = 10; r =  2,22 R =  6,61

A =  - arccos  100,3 B = arccos  30,51 C = arccos  49,19;

m_A = 5 m_B = m_C = ; h_A = 5 h_B = h_C = 6 ; M (; 1) l_B = =

Дополнительные задачи.

1. M (1 ; 1 ; 2 ) 2.  3. 4. S =  =

=  =    =

=   