Three circles of diameter 3cm, 4cm and 6cm are inscribed incide a rectangle, with the middle Circle touching the other two circle as shown. Find the distance AB
Answers
Answer:
15cm.......hope it helps ........mark as brain liest
The distance AB is 3√6 cm
Step-by-step explanation:
The image given in the question is attached below.
Let the name of left most circle be 'A'
Let the name of middle circle be 'B'
Let the name of right most circle be 'C'
The radius of A = 1.5 cm
The radius of B = 2 cm
The radius of C = 3 cm
The distance between the point P and Q is:
PQ = 1.5 + 2 cm = 3.5 cm
The distance between point Q and R is:
QR = 2 + 3 = 5 cm
The distance between the point M and Q is:
MQ = 3 - 2 = 1 cm
The distance between the point N and Q is:
NQ = 2 + 0.5 = 2.5 cm
On applying Pythagoras theorem on circle A and B, we get,
PN = √((PQ)² - (QN)²)
PN = √((3.5)² - (2.5)²)
PN = √(12.25 - 6.25)
∴ PN = √(6)
On applying Pythagoras theorem on circle C and B, we get,
RM = √((QR)² - (MQ)²)
RM = √((5)² - (1)²)
RM = √(25 - 1)
∴ RM = √(24) = √(4 × 6) = 2√6
The distance between 'A' and 'B' is:
AB = √(6) + 2√6
∴ AB = 3√6 cm
