Question

If two equal circles of radius 5 cm have two common tangents AB and CD which touch the circle on A, C and B, D respectively and if CD = 24 cm, find the length of AB.

(a) 27 cm 

(b) 25 cm 

(c) 26 cm 

(d) 30 cm

Answer 1

Answer : (c) 26 cm

Refer to diagram: DOCP ≅ DO′BP 

⇒ OP = O′P 

Let CP = x. Then, PD = 24 – x 

OP² = 5² + x², O′P² = 5² + (24 – x)² 

OP² = O′P² ⇒ 25 + x² = 25 + (24 – x)² 

⇒ x = 12 

∴ OP² = 5² + 12² 

⇒ OP = 13 = O′P 

∴  AB = OO′ = OP + PO′ 

= 13 + 13 = 26 cm.