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Summer Clouds moderators

10/08/2017 at 15:50
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Circles O and P, of radius 16 cm and 4 cm, respectively, are tangent, as shown. Segment NP is tangent to circle O at point N. What is the length of segment NP?
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    Phan Thanh Tinh Coordinator 10/08/2017 at 18:14

    NP is tangent to circle center O at N,so \(NP\perp ON\) at N

    Assume that the circle center O and the circle center P touch each other at M, then O,M,P are collinear.

    => OP = OM + MP = 16 + 4 = 20 (cm)

    Applying the Pythagoras theorem to the right \(\Delta ONP\),we have :

    \(NP=\sqrt{OP^2-ON^2}=\sqrt{20^2-16^2}=\sqrt{144}=12\left(cm\right)\)

    So,the answer is 12 cm

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