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
The answer is C because you can have a triangle with 5,9,n 5,10,n 9,10,n and 5,10,9
The reason why is because the sum of two sides is always larger than the value of the third side.
I hope that this helps.
-3/4 or it could also be -0.75
Answer:
900
Step-by-step explanation:
The figure is a triangular prism
The equation would be V = A * H / 3
V being the volume
A being the area of the pyramids base
H being the height front he base to the top (20)
Base area is 135 (A)
135 * 20 = 2700
2700 divided by 3 = 900
900 is your answer
Area of a circle: πr²
Data:
diameter: 21 cm
radius=diameter/2=21 cm/2=10.5 cm
area of this circle: π(10.5 cm)²=110.25π cm² (≈346.36 cm²)
Answer: area=110.25π cm²
