Question

Calculator 2. Given: In Circle C, RU = SN, CM = 7x+28, CP=14x+7, SP = 173-2. Find the following: VIP b. PN = 49 c. SN - 98 d. CM 49 e. mRO f. CN- Hint? Click here to type

Answer 1

e) arcRO = 54.43

f) CN = 49 sqrt(2)

Solution

7x + 28 = 14x + 7

7x = 21

x = 3

CM = CP = SP = 49

So, PN = 49

SN = 98

Consider △ CPN, it is right angled at P and has CP = PN = 49.

So applying Pythagorean theorem,

CN^2 = CP^2 + PN^2

CN = sqrt ( 49^2 + 49^2) = sqrt (2401+2401) = sqrt (4802)

CN = 49 sqrt(2)

CN = 4972

49 +45 PP AZN

As CPN is isosceles right-angled triangle, ∠PCN = ∠PNC = 45

Similarly in △RMC, as CM = 49 and RU = SN = 2 RM, we get RM = 49, it is also isosceles right-angled.

So ∠ RCM = ∠RCO = 45°

Also CN = RC = CO = 49 sqrt(2) ( radius of the circle)

Length of arc, s = rθ, where r is the radius and θ is the angle swept in radians.

For arc length RO, r = 49 sqrt(2) and θ = 45° * π/180° = π/4

measure of length of arc RO = 49 sqrt(2) * π/4 = 54.43

length of arc RO = 54.43