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Find the length of the common internal tangent PQ. (See diagram)

 

 Apr 6, 2021
 #1
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There are a couple of similar right triangles: APC and BQC

 

AB = 5          AP = 1          AC = x             BQ = 3             BC = 5 - x

AP / AC = BQ / BC

1 / x = 3 / (5 - x)

4x = 5 

x = 1.25

AC = 1.25            BC = 3.75 

PC = sqrt(AC2 - AP2) = 0.75

QC = (PC * BQ) / AP         QC = 2.25

PQ = PC + QC    

PQ = 3 cm

 Apr 7, 2021

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