Common tangent qs
Distance between A and B is 25 cm and distance between P and Q is 24 cm. Diameter of the larger circle is 24 cm.
Q1. What is the ratio of AB:BR?
a. 7 : 5
b. 7 : 6
c. 7 : 10
d. data insufficient
Q2. what is the ratio of area triangle of APR and triangele BQR ?
a. 169 : 36
b. 144 : 25
c. 625 : 144
d. Cant be determined
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hey this is the approach...
1st consider as we know AB=25, PQ=24
this PQ is length of the tangent...for length of the tangent we have formula i.e., pq = sqrt(AB^2 - (R-r)^2)
we have R=12
then by substituting the values....we get...r= 5
let BR=x
the...we have...trngle APR and BQR are similar..... then..
AP/AR= BQ/BR
12/25+x = 5/x
x=125/7
then 1st question......
AB/BR= 25/(125/7) = 7/5 = 7:5
2nd question....
since APR BQR are similar..... ratios of area of triangles= square of their corresponding sides.................
(ar trngle APR)/(ar trngle BQR)= (AP)^2/(BQ)^2 = 12^2/5^2= 144/25
ie.,144:25.............
Little Star
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can u check data plz
Little Star
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