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=}(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=(110^(\circ)-45^(\circ))/(2)=32.5^(\circ).`

To determine m
`m\angle BAD=(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}`