The radius of the circle is 11.1 cm, the radius CM is perpendicular to the chord LK, and MQ measures 3.4 cm. What is the length of the chord LK?

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Answer 1 · 2017-11-03T18:16:11

# LK~~15.99cm.#

Note that, #CQ+QM=CM.#

#rArr CQ=CM-QM=11.1-3.4=7.7cm.#

In the Right- #Delta CQK, /_CQK=90^@.#

#:. CK^2=CQ^2+QK^2.#

Here, #CQ=7.7cm, and, CK"=radius="11.1cm.#

#:. 11.1^2=7.7^2+QK^2.#

#:. QK^2=11.1^2-7.7^2=123.21-59.29=63.92.#

#:. QK=sqrt63.92~~7.995cm.#

Since, a radius, #bot-# to a chord bisects the chord, we have,

#LK=2QK~~2xx7.995=15.99cm.#