In the following diagram A and B are the centres of two different circles. PQR a common tangent. is. Points A, B and R lie on the straight line. Also, AB = 25 cm, PQ diameter of larger circle is 24 cm. Find the ratio of AB : BR.
Answers
Given : A and B are the centres of two different circles. PQR a common tangent Points A, B and R lie on the straight line
AB = 25 cm , PQ = 24 cm
diameter of larger circle is 24 cm
To Find : ratio of AB : BR.
Solution:
ΔRBQ & ΔRAP
∠BRQ = ∠PRQ as B lies on PR
∠BQR = ∠APR = 90° ( Tangent )
=> ΔRBQ ≈ ΔRAP (AA)
BR/AR = BQ/AP = RQ/RP
QR = x BR = y
AR = AB + BR = 25 + y
BR/AR = RQ/RP
=> y / (25 + y) = x/ (24 + x)
=> 24y + xy = 25x + xy
=> 24y = 25x
x/ (24 + x) = BQ/AP
BQ = √y² - x²
=> x/ (24 + x) = √y² - x²/12
=> 12x = (24 + x) √y² - x²
=> 12x = (24 + x) √(25x/24)² - x²
=> 12* 24x = (24 + x) 7x
=> 288 = (24 + x)7
=> 288 = 168 + 7x
=> 7x = 120
=> x = 120/7
24y = 25x
=> 24y = 25 (120/7)
=> y = 125/7
AB = 25
BR = 125/7
=> AB : BR = 25 : 125/7
= 7 : 5
ratio of AB : BR = 7 : 5
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