write the length of AB?
Answers
Answer:
The length of AB is 7.35 c.m.
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 -
{pr}^{2} = {ps}^{2} - {rs}^{2}
{pr}^{2} = {5}^{2} - {1}^{2}
{pr}^{2} = 24
pr = \sqrt{24}
pr = \sqrt[2]{6}
so the length of mb = \sqrt[2]{6}
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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 -
{oq}^{2} = {op}^{2} - {pq}^{2}
{oq}^{2} = {3.5}^{2} - {2.5}^{2}
{oq}^{2} = 12.25 - 6.25
oq = \sqrt{6}
so the length of am = \sqrt{6}
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Finding the length of AB -
AB = MB + AM
AB = MB + AM
AB = 4.9 + 2.45
AB = 7.35 cm.
Hope it help