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Math Help - circle geometry help 2

  1. #1
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    circle geometry help 2

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  2. #2
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    Hello andy69

    The question is shown in the diagram I have attached.

    Proof

    (i) \angle QXB + \angle BXA + \angle AXP = 180^o (angles on a straight line)


    \angle BXA = 90^o (given)


    \therefore \angle QXB + \angle AXP = 90^o


    But \angle PAX + \angle AXP = 90^o (angle sum of \triangle APX)


    \therefore \angle QXB = \angle PAX
    =\angle QBX (angles in same segment)
    (ii) BQ = XQ (isosceles \triangle BQX, from part (i))

    \angle BXC = 90^o (given)


    \therefore X lies on a circle with diameter BC (angle in semicircle)


    But BQ = XQ (proven)


    \therefore Q is the centre of the circle through B, \;X and C


    \therefore BQ = QC


    Grandad
    Attached Thumbnails Attached Thumbnails circle geometry help 2-untitled.jpg  
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  3. #3
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    Quote Originally Posted by Grandad View Post
    Hello andy69

    The question is shown in the diagram I have attached.

    Proof

    (i) \angle QXB + \angle BXA + \angle AXP = 180^o (angles on a straight line)


    \angle BXA = 90^o (given)


    \therefore \angle QXB + \angle AXP = 90^o


    But \angle PAX + \angle AXP = 90^o (angle sum of \triangle APX)


    \therefore \angle QXB = \angle PAX
    =\angle QBX (angles in same segment)
    (ii) BQ = XQ (isosceles \triangle BQX, from part (i))

    \angle BXC = 90^o (given)


    \therefore X lies on a circle with diameter BC (angle in semicircle)


    But BQ = XQ (proven)


    \therefore Q is the centre of the circle through B, \;X and C


    \therefore BQ = QC


    Grandad
    hey thanks for the help you mind me asking how do you attach the pictures?
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  4. #4
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    Hello andy69
    Quote Originally Posted by andy69 View Post
    hey thanks for the help you mind me asking how do you attach the pictures?
    I have a program called MWSnap that enables me to capture any part of the screen, to clipboard. Paste it into Paint; crop as necessary; save as .jpg. Quick and simple. Another example attached!

    Grandad
    Attached Thumbnails Attached Thumbnails circle geometry help 2-untitled.jpg  
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