In the diagram,the chord AB is perpendcular to the diameter CD,AB=70cm and CE=25cm.Find
a)the radius of the circle
b)the area of triangle AOB,where O is the centre of the circle.
ans is:
a)37cm
b)420cm^2
i nid help on how to get the answer.
In the diagram,the chord AB is perpendcular to the diameter CD,AB=70cm and CE=25cm.Find
a)the radius of the circle
b)the area of triangle AOB,where O is the centre of the circle.
ans is:
a)37cm
b)420cm^2
i nid help on how to get the answer.
Hello, tempq1!
$\displaystyle \text{In circle }O:\:\text{chord }AB \perp \text{diameter }CD,\;AB=70\text{cm},\;CE=25\text{cm.}$
Find:
a) the radius of the circle
b) the area of $\displaystyle \Delta AOB$
We have: .$\displaystyle AB = 70 \quad\Rightarrow AE = 35$
. . and: .$\displaystyle CE = 25$
Draw radius $\displaystyle OA = r$
. . Then: .$\displaystyle EO \:=\:r - 25$
In right triangle $\displaystyle AEO\!:\;(r-25)^2 + 35^2 \:=\:r^2$
. . $\displaystyle r^2 - 50r + 625 + 1225 \:=\:r^2 \quad\Rightarrow\quad 50r \:=\:1850$
Therefore: .$\displaystyle \boxed{r \:=\:37\text{ cm}}$
In $\displaystyle \Delta AOB\!:\;\begin{Bmatrix}\text{base} &=& AB &=& 70 \\
\text{height} &=& EO &=& 12\end{Bmatrix}$
Therefore: .$\displaystyle \Delta AOB \;=\;\tfrac{1}{2}bh \;=\;\tfrac{1}{2}(70)(12) \;=\;\boxed{420\text{ cm}^2}$