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
An expression is defined as a set of numbers, variables, and mathematical operations
<h3>What is an Expression?</h3>
In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
The given expression can be simplified as,
A.) 7 3/4 - (√11)/5 = (155-4√11)/20
B.) 7 3/4 ÷ (√11)/5 = 155/(4√11)
C) 7 3/4 + (√16)/5 = 166/20
D.) 7 3/4 + (√16)/5 = 31/5
The option that will result in a rational number is C and D.
Learn more about Expression:
brainly.com/question/13947055
#SPJ1
Answer:
<em>The perimeter is 72 units and the area is 149 square units.</em>
Step-by-step explanation:
has coordinates 
and 
Using the distance formula.........
Length of side 
Length of side 
Length of side 
So, the perimeter of the triangle will be: 
units. <em>(Rounded to the nearest unit)</em>
The height of the triangle for the corresponding base 
is 8.89 units.
<u>Formula for the Area of triangle</u>, 
So, the area of the will be: 
square units. <em>(Rounded to the nearest unit)</em>
