SarkariPYQ

SSC CGL 2024 PYQ — Question 56

SSC CGL - 12 Sep 2024 - Shift 1 • Quantitative Aptitude • Q56

Back to paper

Two circles C1 and C2 touch each other externally. The radius of C1 = 16 cm and the radius of C2 = 8 cm. Find the length (in cm) of their common tangent.

Show answer & explanation

Correct answer: D

Explanation

The correct answer is Option 4 i.e.  16216\sqrt{2}.

We know that,

Length of direct common tangent = √(d2 - (r1 - r2)2)

here,

⇒ d = r1 + r2, r1, r2 = radius of the circles

So,

⇒ r1 = 16 cm, and r2 = 8 cm

So, d = 16 + 8 = 24 cm

Now,

Length of direct common tangent = √(242 - (16 - 8)2)

⇒ √(576 - 64)

⇒ √512 = √4 × 4 × 4 × 4 × 2 = 16√2 cm