Question

In the diagram, HK is tangent to Circle O. If HK is 24mm and the length from H to the
edge of the circle along OH is 18mm, what is the length of the radius of the circle?

Answer 1

Answer:

The length of the radius of the circle is 7 mm

Step-by-step explanation:

see the attached figure to better understand the problem

we know that

If HK is tangent to circle O at point K

then

The radius OK is perpendicular to segment HK and triangle OKH is a right triangle

Applying the Pythagorean Theorem

$OH^2=OK^2+HK^2$

we have

$OH=(r+18)\ mm\\OK=r\ mm\\HK=24\ mm$

substitute

$(r+18)^2=r^2+24^2$

solve for r

$r^2+36r+324=r^2+576$

$36r=576-324\\36r=252\\r=7\ mm$

therefore

The length of the radius of the circle is 7 mm