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The distance from the center of a circle  to a chord lengh of 16 cm is 15 cm. About...

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alexa0048 | Student, Grade 11 | eNoter

Posted May 28, 2013 at 2:33 PM via web

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The distance from the center of a circle  to a chord lengh of 16 cm is 15 cm. About the circle is circumscribed a triangle  with perimeter of 2 m. Calculate the area of the triangle.

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embizze | High School Teacher | (Level 1) Educator Emeritus

Posted May 28, 2013 at 5:12 PM (Answer #1)

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(1) We are given that the distance from the center of the circle to a chord of length 16cm is 15cm.

Now a diamter drawn perpendicular to a chord bisects the chord. So draw a diamter perpendicular to the chord. This creates a right triangle; one leg is 15cm (given), one leg is 8cm (chord is bisected), and the hypotenuse is the radius of the circle. We can regonize that 8-15-17 is a primitive Pythagorean triple, or use the Pythagorean theorem `r^2=15^2+8^2=289 ==> r=17` .

The radius of the circle is 17cm.

(2) If the triangle is equilateral, then the area can be found by `A=1/2ap` where a is the apothem and p is the perimeter. The perimeter is given as 2m=200cm. The apothem will be the radius of the circle. (The apothem is the segment drawn from the center of a regular polygon perpendicular to a side. The center of the triangle will be the center of the inscribed circle, and since a radius drawn to a point of tangency is perpendicular to the tangent this is the apothem.)

So the area of the triangle will be `A=1/2(200)(17)=1700"cm"^2`

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