Circles are cool!

Geometry Level 2

Consider two parallel chords of a circle $AB$ and $CD$ where $AB$ is a diameter.It is known that $AC=13$ and $AD=84$ .Find the radius of the circle.

The answer is 42.5.

1 solution

Chew-Seong Cheong
Dec 2, 2014

If the two chords $AB$ and $CD$ are parallel to the $x$ -axis, then they are symmetrical along the $y$ -axis through the origin of the circle. Due to the symmetry, $BD = AC = 13$ . Since $AB$ is a diameter, $\angle ADB=90^\circ$ . Therefore the diameter of the circle $D = \sqrt{13^2+84^2} = 85$ and the radius $r=\boxed {42.5}$ .

I still do not know why that angle is 90 degrees? I cannot justify it?

Adam Staples - 6 years, 6 months ago

Sorry, I didn't explain it. Angle in a semicircle is always $90^\circ$ . Since $AB$ is a diameter and $D$ is on the circumference, therefore, $\angle ADB = 90^\circ$ .

Chew-Seong Cheong - 6 years, 6 months ago

Thanks, I did not know that! http://www.savory.de/maths18.htm I found an amazing proof here for anyone interested!

Adam Staples - 6 years, 6 months ago

@Adam Staples – That proof is available in 9th standard maths.

Dheeraj Dhillon - 5 years, 5 months ago

Angle in front of Diameter is 90° according to circle properties.

Azeem Haïder - 5 years, 9 months ago

Circles are cool!

The answer is 42.5.

1 solution

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