Mathematics Question and Solution

By Ogheneovo Daniel Ephivbotor
1st August, 2023

Sir Mike Ambrose is the author of the question.

Let r be the radius of the three congruent circles.


Calculating r.


(9+r)² = (9-r)²+(9-3r)²

81+18r+r² = 81-18r+r²+81-54r+9r²

36r = 81-54r+9r²

9r²-90r+81 = 0

r²-10r+9 = 0

r ≠ 9 units.

r = 1 unit.


a² = (2*9²)

a = 9√(2) units.


b² = 2(1)²

b = √(2) units.


c = a-b

c = 8√(2) units.


(8√(2))² = 10²+2²-2*2*10cosd

128 = 104-40cosd

cosd = (104-128)/40

d = 126.86989764584°


(8√(2)/sin126.86989764584) = (2/sine)

e = 8.13010235416°


f = 180-d-e

f = 45°


Therefore;


A Area to 2 decimal places square cm is;


2(0.5*8√(2)*2sin45 - ⅛(π) - 126.86989764584π/360 - 8.13010235416π*81/360)


= 2(8-0.3926990817-1.10714871779-5.74683071147)


= 2(0.75332148904)

= 1.50664297808 cm²

≈ 1.51 cm²

Tags:

WhatsApp Google Map

Safety and Abuse Reporting

Thanks for being awesome!

We appreciate you contacting us. Our support will get back in touch with you soon!

Have a great day!

Are you sure you want to report abuse against this website?

Please note that your query will be processed only if we find it relevant. Rest all requests will be ignored. If you need help with the website, please login to your dashboard and connect to support