Question

Diagram 5 shows a semicircle with centre O.It is given that the arc length of PQ=9cm and the perimeter POQ=19cm. Calculate value of Ø in degree

Answer 1

Given:

The perimeter is 19 cm.

Acr length is 9 cm.

The perimeter of circle is calculated as,

`\begin{gathered} \text{Perimeter POQ=PO+OQ+length of PQ} \\ 19=r+r+9 \\ 10=2r \\ r=5 \end{gathered}`

The arc length is calculated as,

`\begin{gathered} \text{Arc length =}\theta*(\pi)/(180)* r \\ 9=\theta*(\pi)/(180)*5 \\ 9=\theta*(\pi)/(36) \\ \theta=103.13 \\ \theta\approx103^(\circ) \end{gathered}`

Answer:

`\theta=103^(\circ)`