No this is not a triangle. With these lengths
Answer:
The radius of the circle P = 2√10 = 6.325
Step-by-step explanation:
∵ AB is a tangent to circle P at A
∴ (AB)² = BC × BE
∵ BC = 8 , AB = 12 , ED = 6
∵ BE = ED + DC + CB
∴ BE = 6 + CD + 8 = 14 + CD
∴ (12)² = 8 × (14 + DC) ⇒ (12)²/8 = 14 + CD ⇒ CD = (12)²/8 - 14
∴ CD = 4
Join PC and PE (radii)
In ΔBDC and ΔPDE ⇒ ∵ ∠PDC = Ф , ∴ ∠PDE = 180 - Ф
Use cos Rule:
∵ r² = (PD)² + (DC)² - 2(PD)(DC)cosФ
∴ r² = 16 + 16 - 32cosФ = 32 - 32cosФ ⇒ (1)
∵ r² = (PD)² + (DE)² - 2(PD)(DE)cos(180 - Ф) ⇒ cos(180 - Ф) = -cosФ
∴ r² = 16 + 36 + 48cosФ = 52 + 48cosФ ⇒ (2)
∵ (1) = (2)
∴ 32 - 32 cosФ = 52 + 48cosФ
∴ 32 - 52 = 48cosФ + 32cosФ
∴ -20 = 80cosФ
∴ cosФ = -20/80 = -1/4
∴ r² = 32 - 32(-1/4) = 32 + 8 = 40
∴ r = √40 = 2√10 = 6.325
Answer:
m = -1
Step-by-step explanation:
First write the line in slope intercept form y = mx+b where m is the slope and b is the y intercept
x-y = 6
subtract x from each side
-y = -x+6
Multiply each side by -1
y = x-6
The slope is 1
Perpendicular lines have slopes that multiply to -1
m * 1 = -1
m = -1
The slope of the perpendicular line is -1
Answer:
x = 13
Step-by-step explanation:
Sum or interior angles of a triangle is 180,
6x + 19 + 5x - 15 + 3x - 6 = 180
6x + 5x + 3x + 19 - 15 - 6 = 180
14x + 19 - 21 = 180
14x - 2 = 180
14x = 180 + 2
14x = 182
x = 182 / 14
x = 13
Answer:
1050
Step-by-step explanation:
