# (Another) Grade 11 High School Circles Question

• Nov 30th 2008, 10:38 AM
s3a
(Another) Grade 11 High School Circles Question
"Isosceles triangle ABC is inscribed in a circle with radius 5cm. Base BC measures 8cm. Find the length of the other two sides of the triangle."

4Sqrt(5)cm or ~ 8.94cm

Can someone show it to me visually so that I know how to interpret the question because when I do it, I get a different answer.
• Nov 30th 2008, 11:00 AM
masters
Quote:

Originally Posted by s3a
"Isosceles triangle ABC is inscribed in a circle with radius 5cm. Base BC measures 8cm. Find the length of the other two sides of the triangle."

4Sqrt(5)cm or ~ 8.94cm

Can someone show it to me visually so that I know how to interpret the question because when I do it, I get a different answer.

See diagram.

Drop a perpendicular from the vertex angle to the base which bisects the base.

Use the Pythagorean theorem to find the distance from the center to the base.

$\displaystyle 5^2=4^2+x^2$

$\displaystyle 25-16=x^2$

$\displaystyle 9=x^2$

$\displaystyle x=3$ This is the length of the altitude.

Use Pythagorean theorem again to find AC.

$\displaystyle (AC)^2=4^2+8^2$

$\displaystyle (AC)^2=80$

$\displaystyle AC=\sqrt{80}$

$\displaystyle AC=\sqrt{16\cdot 5}$

$\displaystyle AC=4\sqrt{5}$