Question

In the given figure RTP and STQ are common tangents to the two circles with centres A and B. The radii of the two circles are 3 cm long are 5 cm long respectively.
If ST : TQ =1 : 3 and RT = 4 cm, calculate (a) the length of-QT (b) the length of AB

Answer 1

We know that the the two centres, and the point of intersection of tangents are collinear and they lie on a straight line.

Let $AT=x$

In triangle ATS, using pythagoras theorem, we get that

$ST=\sqrt{(x^2-9)}=RT=4$ (as lenght of tangents drawn from an external point is same)

$\Rightarrow x=5cm$

(a) It is given that $\frac{ST}{TQ}=\frac{1}{3}$

$\Rightarrow QT=3\times ST=12cm$

(b) $AB=AT+BT$

$AT=x=5cm$

$BT=\sqrt{(Q{T}^2+B{Q}^2)}$= 13cm

$AB=18cm$.