← Quantitative Aptitude

Geometry (Tangents) — Questions with Solutions

2 solved Geometry (Tangents) questions from Quantitative Aptitude, as asked in SSC CGL and other SSC exams. Read the answer and explanation below, then practise the full set in the practice section.

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Q1. Two circles of radii $18\text{ cm}$ and $12\text{ cm}$ touch each other externally. Find the length of their direct common tangent.

$18\text{ cm}$ और $12\text{ cm}$ त्रिज्या वाले दो वृत्त एक दूसरे को बाह्य रूप से स्पर्श करते हैं। उनकी सीधी उभयनिष्ठ स्पर्श रेखा (direct common tangent) की लंबाई ज्ञात कीजिए।

  1. A. $15\sqrt{6}$
  2. B. $10\sqrt{6}$
  3. C. $12\sqrt{6}$
  4. D. $18\sqrt{6}$

Solution

When circles touch externally, DCT = $2\sqrt{r_1 r_2} = 2\sqrt{18 \times 12} = 2\sqrt{216} = 2 \times 6\sqrt{6} = 12\sqrt{6}\text{ cm}$.

Q2. The distance between the centres of two circles of radii 22 cm and 10 cm is 37 cm. If the points of contact of a direct common tangent to these circles are M and Q, then find the length of the line segment MQ.

  1. A. 35 cm
  2. B. 39 cm
  3. C. 29 cm
  4. D. 25 cm

Solution

Direct Common Tangent length = √[d² - (R-r)²] = √[37² - 12²] = √[1369 - 144] = √1225 = 35 cm.