PQRS is a common diameter of
three circles. The area of the
middle circle is the average of
the area of the other two. If PQ
= 2 and RS = 1 then the length
QR is
Answers
ANSWER:
Given
- PQRS is the common diameter of all the three circles
- PQ = 2 , RS = 1 , QR = ?
- Area of circle which has diameter PR = Average of other circles =
= Ar(Circle no.1) + Ar(Circle no.2) /2
♦ We know that:
Area of Circle = πr²
Middle circle's (Circle no.2)
→ Diameter = PR = PQ + QR = 2 + QR
→ Radius = Diameter/2 = 2 + QR/2
First circle's (Circle no.1)
→ Diameter = PQ = 2
→ Radius = 2/2 = 1
→ Area = π(1)² = π = 3.14
Third circle's (Circle no. 3)
→ Diameter = PS = PQ + QR + RS = 2 + QR + 1
PS = 3 + QS
→ Radius = 3 + QR/2
Ar(Circle no.2) = Ar(circle no. 1) + Ar(circle no. 3)/2
★ π(2 + QR/2)² = 3.14 + π(3 + QS/2)²
★ π[(2 + QR)²/2²] = 3.14 + π[(3 + QS)²/2²)]
Using
(a + b)² = a² + 2ab + b²
★ π(4 + 4QR + QR²/4) - π(9 + 6QR + QR²/4) = 3.14
★ π(4 + 4QR + QR² - (9 + 6QR + QR²)/4) = 3.14
★ π( 4 + 4QR + QR² - 9 - 6QR - QR²/4) = 3.14
★ -5 - 2QR/4 = 3.14/3.14
★ - 5 - 2QR = 4
★ - 2QR = 4 + 5
★ QR = 9/-2
★ QR = - 4.5
Hence, distance cannot be negative so, QR = 4.5
Hence, QR = 4.5
Answer:
hope it helps !!
Step-by-step explanation:
QR=5