Select the correct answer. Which point lies on a circle with a radius of 5 units and center at P(6, 1)?
A. Q(1,11)
B. R (2,4)
C. S (4, -4)
D. T(9,-2)

B

Step-by-step explanation:

An equation of a circle:

(x - a)² + (y - b)² = r²

(a; b) - a coordinates of a center

r - a radius

r = 5; P(6; 1) ⇒ a = 6 and b = 1

therefore

(x - 6)² + (y - 1)² = 5²

check:

A) Q(1; 11)

L = (1 - 6)² + (11 - 1)² = (-5)² + 10² = 25 + 100 = 125

R = 25

L ≠ R

B) R(2; 4)

L = (2 - 6)² + (4 - 1)² = (-4)² + 3² = 16 + 9 = 25

R = 25

L = R - CORRECT

C) S(4; -4)

L = (4 - 6)² + (-4 - 1)² = (-2)² + (-5)² = 4 + 25 = 29

R = 25

L ≠ R

D) T(9; -2)

L = (9 - 6)² + (-2 - 1)² = 3² + (-3)² = 9 + 9 = 18

R = 25

L ≠ R

B) R(2; 4).

  21.3

step-by-step explanation:

multiplying the given equation by c/sin(25°), we get

  c = 9/sin(25°) ≈ 21.2958 ≈ 21.3

we assume "c" is the length of ab, the side opposite angle c in triangle abc.

the sum of the lengths of any two sides of a triangle is greater than the length of the third side. if you take the three sides of a triangle and add them in pairs, the sum is greater than (not equal to) the third side. if that is not true, then it is not possible to construct a triangle with the given side lengths.

step-by-step explanation: