Two circles have radii of 8 cm and 3 cm. The distance between their centers is 15 cm. What is the length of a direct common tangent?
Two circles have radii of 8 cm and 3 cm. The distance between their centers is 15 cm. What is the length of a direct common tangent?
दो वृत्तों की त्रिज्याएँ 8 सेमी और 3 सेमी हैं। उनके केंद्रों के बीच की दूरी 15 सेमी है। सीधे स्पर्श रेखा की लंबाई क्या है?
Detailed Solution & Logic
Correct Answer:
$10\sqrt{2}cm$
Given:
Radius of first circle $r_1 = 8$ cm, radius of second circle $r_2 = 3$ cm, and distance between centers $d = 15$ cm.
For the length of a direct common tangent, we use the formula:
Length = $\sqrt{d^2 - (r_1 - r_2)^2}$
Substitute the values:
Length = $\sqrt{15^2 - (8 - 3)^2}$
= $\sqrt{225 - 25}$
= $\sqrt{200}$
= $10\sqrt{2}$
Final Answer: $10\sqrt{2}$ cm
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