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Question : A transverse common tangent is drawn to two circles of radius 8.5 cm and 5.5 cm. The centres of the two circles are 18 cm apart. What is the length (in cm) of the tangent?

Option 1: $10 \sqrt{3}$

Option 2: $10 \sqrt{2}$

Option 3: $8 \sqrt{2}$

Option 4: $8 \sqrt{3}$


Team Careers360 3rd Jan, 2024
Answer (1)
Team Careers360 17th Jan, 2024

Correct Answer: $8 \sqrt{2}$


Solution : Given: The Radii of circles are 8.5 cm and 5.5 cm and the length between circles is 18 cm.
$r_1=8.5\ \text{cm}$
$r_2=5.5\ \text{cm}$
$d=18\ \text{cm}$
The length of a transverse common tangent
$=\sqrt{d^2−(r_1+r_2)^2}$
$=\sqrt{(18)^2−(8.5+5.5)^2}$
$=\sqrt{324−196}$
$=\sqrt{128}=8 \sqrt{2}\ \text{cm}$
Hence, the correct answer is $8 \sqrt{2}\ \text{cm}$.

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