calculate PQ, if AB = 8cm

Question

AC is a transverse common tangent to two circles with centres P and Q and  of radii 6cm and 3cm respectively 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Answer 1

Pranav,

 

First of all, let's emend the question to state "AB is a common...

 

Draw in the sides of quadrilateral ABPQ and the line QM parallel to BA and meeting AP at M.

 

Angles PAB and ABQ are right angles, so ABQM is a rectangle and therefore AM=3 and MQ=8

 

Consider the right triangle PMQ and apply Pythagoras' Theorem:  PQ^2=MP^2+MQ^2

 

PQ^2=64+9

 

PQ=sqrt(73)

 

You might want to prove to yourself that the circles intersect...Although you drew the diagram initially, perhaps

you did not know whether to draw the circles disjoint, tangent or intersecting?