1 answer

How length of /AC/ = ?

Question:

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Answers

#AC=16# cm

Explanation:

As two tangent segments to a circle from an external point are equal in length, #=> CD=CT=8#,
#=> BC=BD-CD=12-8=4#,
As #CT# is tangent to circle centered at #O_1#, and #CBA# is the secant line, by tangent-secant theorem, we get:
#CT^2=CA*CB#
#=> 8^2=CAxx4#,
#=> AC=64/4=16# cm

Proof of tangent-secant theorem is available in the link below:
https://socratic.org/questions/let-m-be-a-point-and-c-a-circle-m-doesn-t-belong-to-the-c-let-a-and-b-be-points-#471096

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