Question

Two circles of radii 25 cm and 9 cm touch each other externally. Find the length of the direct common tangent.

Answer 1

Let the two circles with centers A, B and of radii 25 cm and 9 cm touch each other externally at point C. Then, AB = AC + CB = (25 + 9) cm = 34 cm.

Let PQ be the direct common tangent. 

∴ BQ ⊥ PQ and AP ⊥ PQ. 

Draw BR ⊥ AP. 

Then BRPQ is a rectangle. (Tangent ⊥ radius at the point of contact)

In ∆ABR, AB² = AR² + BR² (Pythagoras’ Theorem) 

⇒ (34)² = (16)² + BR² 

⇒ (BR)² = 1156 – 256 = 900 

⇒ BR = \(\sqrt{900}\)cm  =  30 cm

∴ PQ = BR = 30 cm.