Question

Shown below are three circles, P, Q and R. Their centres are C1 , C2 and C3 respectively.
The radius of circle P is 2 cm.

What is the DIAMETER of circle R?

Answer 1

Step-by-step explanation:

ΔPC

1

A,ΔPC

2

B,ΔPC

3

C in one angle is 90

o

& angle P is common, then above triangle will be similar.

Hence for ΔPC

1

A & ΔPC

2

B

r

1

PA

=

r

2

PB

.........(i)

ΔPC

2

B & ΔPC

3

C

r

2

PB

=

r

3

PC

.........(ii)

we know that if tangents are drawn from an external point P to 3-circles

PA⋅PC=PB

2

or

PB

PA

=

PC

PB

r

2

r

1

=

r

3

r

2

r

2

=

r

1

r

3

.