Measure of CD

Geometry Level 3

Given two circles A A and B B that are tangent to each other with radii 4 and 6 respectively. A line is tangent to these circles at points C C and D D . What is the measure of segment C D CD ? (Round answer to three decimal places.)


The answer is 9.798.

Hana Wehbi by Hana Wehbi , 51, USA

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2 solutions

Relevant wiki: Pythagorean Theorem

Applying pythagorean theorem on △ D C E \triangle DCE , we have

( C D ) 2 = 1 0 2 − 2 2 = 100 − 4 = 96 \large (CD)^2=10^2-2^2=100-4=96 ⟹ \large \color{#20A900}\implies C D = 96 = \large CD=\sqrt{96}= 9.798 \large \color{#D61F06}\boxed{9.798}

2 Helpful 0 Interesting 0 Brilliant 0 Confused

Thank you. Nice and clear.

Hana Wehbi - 3 years, 11 months ago
Ahmad Saad
Jul 6, 2017

1 Helpful 0 Interesting 0 Brilliant 0 Confused

Thank you. How did you draw your figure? Any particular software or online download.

Hana Wehbi - 3 years, 11 months ago

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