Question

1. AC is a diameter of the circle.Find measure of AEDFind measure of BCEFind length of ABFind length of CD2. AC is tangent to circle O.Find the lengths of the segments to the nearest hundredth.AO=DC=

Answer 1

80+x+45=180 (sum of angles on a straight line)

x=180-80-45

x=55.

`\begin{gathered} \text{Thus,} \\ i)\text{ measure of AED=80+x} \\ m\text{ AED=80+55} \\ mAED=135^O \end{gathered}`
`\begin{gathered} ii)\text{ measure of BCE=90+45+55} \\ \text{m BCE=190}^0 \end{gathered}`
`\begin{gathered} iii)\text{Length of arc AB=}(\theta)/(360)*2\pi r \\ \text{where }\theta\text{ is the angle subtended by the arc} \\ ^(\prime)r^(\prime)\text{ is the radius.} \\ \text{The radius of AB is 16. The angle subtended by AB is 'y'. Let's find 'y'.} \\ y=360-90-45-55-80=90^0 \\ \text{Thus,} \\ L_{arc\text{ AB}}=(90)/(360)*2*3.142*16.\text{ Take }\pi\text{ to be 3.142} \\ L_{arc\text{ AB}}=25.136 \end{gathered}`
`\begin{gathered} \text{Length of arc CD=}(\theta)/(360)*2\pi r \\ \theta=45^0,\text{ for arc CD.} \\ r=16.\text{ The radius is constant} \\ L_{arc\text{ CD}}=(45)/(360)*2*3.142*16 \\ L_{arc\text{ CD}}=12.568 \end{gathered}`