Answered

Find the best solutions to your questions at Westonci.ca, the premier Q&A platform with a community of knowledgeable experts. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently. Experience the convenience of finding accurate answers to your questions from knowledgeable experts on our platform.

A chord is 5 inches from the center of a circle whose diameter is 26 inches. What is the number of centimeters in the length of the chord?

Sagot :

DavidOrrell
First of all, sorry for not including a picture - I hope I can describe this well enough:

Call the centre of the circle O, the chord AB (touching the circumference at A and B) and the midpoint of AB M. From circle theorems, we know that a radius, passing through the midpoint of a chord, will be perpendicular to it. Therefore we have a right-angled triangle OMA, with the hypotenuse OA forming the radius of length 13in, the line OM being 5in as stated in the question, and the side AM being an unknown.

By Pythagoras' theorem, AM = √(13^2 - 5^2) = 12in (it's a 5,12,13 Triple)

Because M is the midpoint of AB, this value needs to be doubled to get the length of AB as 24in. One inch is 2.54cm (3sf), so the length of the chord is:

24 * 2.54 = 60.96cm, which rounds to 61.0cm (3sf)

I hope this helps
Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. We're glad you visited Westonci.ca. Return anytime for updated answers from our knowledgeable team.