Question

If two non intersecting circles of radii 15cm and 9 cm have their centres 30 cm apart find the transverse common tangent

Answer 1

Answer:

18 cm

Step-by-step explanation:

We are  given that

Radius of two circles are 15 cm and 9 cm.

The distance between the circles of two centers=30 cm

$\triangle APC\; and \;\triangle BQC$

$\angle PAC=\angle QBC=90^{\circ}$ (Radius is perpendicular to tangent)

$\angle PCA=\angle QCB$ (Vertical opposite angles )

$\triangle APC\sim\triangle BQC$

By AA postulate

$\frac{PC}{QC}=\frac{PA}{QB}=\frac{9}{15}=\frac{3}{5}$

$PC=\frac{3}{5}QC$

$PC+QC=30$

$\frac{3}{5}QC+QC=30$

$\frac{8QC}{5}=30$

$QC=30\times \frac{5}{8}=18.75 cm$

$PC=\frac{3}{5}\times 18.75=11.25 cm$

$AC=\sqrt{PC^2-PA^2}=\sqrt{(11.25)^2-81}=6.75 cm$

$BC=\sqrt{QC^2-QB^2}=\sqrt{(18.75)^2-(15)^2}=11.25 cm$

$AB=AC+BC=6.75+11.25=18 cm$

Hence, the transverse common tangent=18 cm

Answer 2

Answer:

18 cm

Step-by-step explanation:

Hope this will help you