Question
Fri October 26, 2012 By: Ashrene

TP and T'Q are parallel tangents to a cicle with radius r , with T and T' the points of tangency.PT''Q is a third tangent with T'' as point of tangency.the centre of the circle is o and it is joined to T'' to form radius r.if TP=4,T'Q=9 then find r

Expert Reply
Fri November 09, 2012
Since from P the tangents are PT and PT''
So, PT=PT''=4
 
Similarly,
QT'=QT''=9
 
So, PQ=PT''+QT'' = 9+4 =13
 
Now, TT'=r+r = 2r
 
And The difference of T'Q-PT= 9 - 4 = 5
 
So, PQ2=TT'2 + (T'Q- TP)2
Or, 4r2+25=169
 
or, r2=36
or r=6 is the answer.
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