Question

What is the length of AB ?
3 cm
4 cm
6 cm--
B​

Answer 1

Answer:

7.35 cm

Step-by-step explanation:

Given - diameter = 3 cm, so radius = 3/2 = 1.5 cm  

Given - diameter = 4 cm, so radius = 4/2 = 2 cm  

Given - diameter = 6 cm, so radius = 6/2 = 3 cm  

Finding the length of MB -  

Radius of 2 circles = 3 cm and 2 cm  

PS = 2 + 3 = 5 cm.  

SR = 3 - 2 = 1 cm .  

∆ PRS is a right angle triangle -  

Finding the length of PR^2 -

pr² = ps² - rs²

pr² = 5² - 1²

pr² = 24

pr = √24

pr =  2√6

so the length of mb = 2√6

finding the length of AM

Finding the length of AM -  

Radius of 2 circles = 1.5 cm and 2 cm  

OP = 1.5 + 2 = 3.5 cm  

PQ = MN - PN - MQ = 6 - 2 - 1.5 = 2.5  

PQ = 2.5 cm  

∆ OQP is a right angle triangle .  

Finding the length of OQ^2 -  

oq² = op² - pq²

oq² = 3.5² - 2.5²

oq² = 12.25 -  6.25

oq = √6

so the length of am = √6

Finding the length of AB -  

AB = MB + AM  

AB = MB + AM  

AB = 4.9 + 2.45  

AB = 7.35 cm