Multiple choice

Two circles having radius a cm and b cm touch each other externally. Another circle whose radius is c cm touches both the circles and also their common tangent. Which statement will be true? दो वृत की त्रिज्या a सेमी और b सेमी हैं एक दूसरे को बाहरी स्पर्श करते हैं | एक और वृत जिसकी त्रिज्या c सेमी है इन दोनों वृत और उभयनिष्ठ स्पर्श रेखा को भी स्पर्श करता है |कौन सा वाक्ये सही होगा ?

  1. √a + √b = √c

  2. √ab + √bc = √ac

  3. √b + √c = √a

  4. √bc + √ac = √ab
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

For two circles of radii a and b touching externally, with a third circle of radius c touching both circles and their common external tangent, the relationship is derived from the formula for a Soddy circle: 1/√c = 1/√a + 1/√b. Rearranging gives √c = √ab/(√a + √b). Option D (√bc + √ac = √ab) is algebraically equivalent to this relationship and is the correct answer.

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