Question

Two circles with centre A and B are touching externally. A circle with centre C touches both externally.Suppose AB = 3 cm,BC = 3 cm and CA = 4 cm .Find the radii.

Answer 1

We have AB = 3 cm, BC = 3 cm and CA = 4 cm
By adding all these, we get:
AB + BC + AC = 3 + 3 + 4 = 10 cm
$\Rightarrow$AP + PB + BR + RC + CQ + QA = 10
$\Rightarrow$AP + PB + PB + CQ + CQ + AP = 10
$\Rightarrow$2AP + 2PB + 2CQ = 10
$\Rightarrow$AP + PB + CQ = 5 ...(i)

We have AP+ PB = AB = 3
Putting this value in (i), we get:
3 + CQ = 5
$\Rightarrow$CQ = 2 cm
Also, AQ+ CQ = AC = 4
⇒ AP + CQ = 4
Putting this value in (i), we get:
4 + PB = 5
$\Rightarrow$PB = 1 cm

Now, putting the values of CQ and PB in (i), we get:
AP + 1 + 2 = 5
∴ AP = 2 cm