Question

A and B are centres of circles of radii 9 cm and 2 cm such that
AB = 17 cm and C is the centre of the circle of radius r сm which
touches the above circles externally. If ZACB = 90°, write an
equation in r and solve it.​

Answer 1

Answer:

AC=9+rcm

AB=17cm

BC=r+2cm

AB

2

=AC

2

+BC

2

⇒17

2

=(r+9)

2

+(r+2)

2

⇒r

2

+81+18r+r

2

+4+4r=289

⇒2r

2

+22r−204=0

⇒r

2

+11r−102=0

⇒r

2

+17r−6r−102=0

⇒r(r+17)−6(r+17)=0

⇒(r+17)(r−6)=0

⇒r=6cm.