Question

Part I: A secant is a line or segment thatpasses through a circle in two places. In thediagram above, find the m< ACE which isformed by two secants.1. Determine the method of finding themACE by circling one of the statementsbelow.2. Use the relationship you established inpart 1 to find the m

Answer 1

To answer this question we will use the two secants theorem, the two secants theorem states:

$angle\text{ formed by two secants=}\frac{1}{2}(diffrence\text{ betw}een\text{ the arcs formed).}$

Therefore, we can establish the following relationship:

$m\angle ACE=\frac{m\hat{AE}-m\hat{DB}}{2}\text{.}$

Substituting the given values for the arcs, we get:

$m\angle ACE=\frac{110^{\circ}-45^{\circ}}{2}=32.5^{\circ}.$

To determine m$m\angle BAD=\frac{1}{2}(45^{\circ}-0^{\circ})=22.5^{\circ}.$

Answer:

$\begin{gathered} m\angle ACE=\frac{m\hat{AE}-m\hat{DB}}{2}, \\ m\angle ACE=32.5^{\circ}, \\ m\angle BAD=22.5^{\circ}. \end{gathered}$