# Angle between two chords

**Problem**

Chords AB and AC are drawn on a circle of radius 10 inches. Find the angle between the chords if the arc BAC is 28 inches long.

**Solution**

By ratio and proportion

$\dfrac{28}{\beta} = \dfrac{2\pi (10)}{360^\circ}$

$\dfrac{28}{\beta} = \dfrac{2\pi (10)}{360^\circ}$

$\beta = 160.43^\circ$

$\alpha = 360^\circ - \beta$

$\alpha = 360^\circ - 160.43^\circ$

$\alpha = 199.57^\circ$

$\theta = \frac{1}{2}\alpha$

$\theta = \frac{1}{2}(199.57^\circ)$

$\theta = 99.78^\circ$