Question

In the given figure, AT and BT are the two tangents at A and B respectively. CD is also a tangent at P.

There are some more circles touching each other and the tangents AT and BT also. Which one of the following is true? 

(a) PC + CT = PD + DT 

(b) RG + GT = RH + HT 

(c) PC + QE = CE 

(d) All of these

Answer 1

Answer : (d) All of these

Since the lengths of the tangents from the same external point are equal, AT = BT 

AC = PC and BD = DP 

∴ AT = BT ⇒ TC + CA = TD + DB 

⇒ TC + PC = TD + PD 

Hence option (a) is true. 

Similarly, we can prove the relations in option (b) and (c) for other circles also.