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Math Help - need help for circles properties question

  1. #1
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    need help for circles properties question

    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.
    Last edited by tempq1; May 1st 2010 at 12:39 AM.
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  2. #2
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    Quote Originally Posted by tempq1 View Post
    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.
    Have you learnt the Cartesian equation of a circle? (ie x^2 + y^2 = r^2) Or are you studying circle geometry?
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  3. #3
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    Quote Originally Posted by tempq1 View Post
    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.
    Hi Tempq,

    Use the property of intersecting chords AE xBE =CE xDE It's very easy then.

    bjh
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  4. #4
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    Hello, tempq1!

    \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 \Delta AOB



    We have: . AB = 70 \quad\Rightarrow AE = 35
    . . and: . CE = 25

    Draw radius OA = r
    . . Then: . EO \:=\:r  - 25

    In right triangle AEO\!:\;(r-25)^2 + 35^2 \:=\:r^2

    . . r^2 - 50r + 625 + 1225 \:=\:r^2 \quad\Rightarrow\quad 50r \:=\:1850

    Therefore: . \boxed{r \:=\:37\text{ cm}}



    In \Delta AOB\!:\;\begin{Bmatrix}\text{base} &=& AB &=& 70 \\<br />
\text{height} &=& EO &=& 12\end{Bmatrix}

    Therefore: . \Delta AOB \;=\;\tfrac{1}{2}bh \;=\;\tfrac{1}{2}(70)(12) \;=\;\boxed{420\text{ cm}^2}

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