M and N are respectively, the centres of two circles of…

M and N are respectively, the centres of two circles of radii 12 cm and 8 cm. QR is the common tangent to the circles. If MN = 16 cm, then what will be the length of QR?

Show answer & explanation

Correct answer: B

Explanation

The correct answer is option 2 i.e. $4\sqrt{15}$ cm.

Given, distance between the centres, MN = 16 cm

Radii, r₁ = 12 cm and r₂ = 8 cm

Direct common tangent, QR = $\sqrt{d^2 - (r_1 - r_2)^2}$

According to the given question,

QR = $\sqrt{16^2 - (12 - 8)^2}$

⇒ QR = $\sqrt{256 - 16}$

⇒ QR = $\sqrt{240}$

⇒ QR = $4\sqrt{15}$ cm

SSC CGL 2024 PYQ — Question 72