Find length of a chord of a circle with radius $13$ cm given position of a point located on the chord.

Question

A point located on a chord of a circle is 8 cm from one endpoint of the chord and 7 cm from the center of the circle. If a radius of this circle is 13 cm long, how long is the chord, in cm?

Please help! I'm not sure where to start.

Answer 1

Hint:

Applying the Pythagorean theorem twice

$$h^2 = 7^2 - x^2 = 13^2 - (8+x)^2$$

where you have one right angled triangle with sides $x$ and $h$ and hypotenuse $7$ and another right angled triangle with sides $8+x$ and $h$ and the radius of $13$ is the hyptenuse.

chord $= 2 \cdot (8+x)$