Question

In the circle above, RV and SW are chords which intersect at point T. If ST = 4 ft, TV = 8 ft, and TW = 12 ft, what is the length of RT?

Answer 1

6 ft

Explanation:

The product of lengths from the point of intersection of the chords to the circle is a constant. For these chords, that constant is ...

ST·TW = (4 ft)(12 ft) = 48 ft²

Then RT can be found from ...

RT·TV = 48 ft²

RT = (48 ft²)/TV = (48 ft²)/(8 ft)

RT = 6 ft