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Two circles have radii 14 cm and 6 cm. If the length of a direct common tangent is 24 cm, what is the distance between their centers?

1. 9 \sqrt{10} cm
2. 8 \sqrt{10} cm
3. 12 \sqrt{10} cm
4. 8 cm

Correct answer: 8 \sqrt{10} cm

Solution

For two circles with a direct common tangent, the distance between centers satisfies \(d^2 = l^2 + (r_1-r_2)^2\). Here, \(l=24\) and \(r_1-r_2=8\), so \(d^2 = 24^2 + 8^2 = 640\). Thus \(d = \sqrt{640} = 8\sqrt{10}\) cm.

Related SSC CGL (Prelims) General questions

• The distance between the centres of two circles is $d$. The lengths of the direct and transverse common tangents are $L$ and $M$ respectively. If $L^2 + M^2 = 320$ and the sum of the squares of the radii is 160, what is $d$?
• Two parallel chords of lengths 20 cm and 14 cm lie on the same side of the centre of a circle. The distance between them is 3 cm. What is the radius of the circle?
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