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Math Help - Geometry (1)

  1. #1
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    Geometry (1)

    In the diagram , X ,Y and Z are the points of contact of tangents BC , CA and AB respectively to a circle with centre O . If angle ACB is a right angle , prove that angle AOB =135 degree .
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  2. #2
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    Hello thereddevils
    Quote Originally Posted by thereddevils View Post
    In the diagram , X ,Y and Z are the points of contact of tangents BC , CA and AB respectively to a circle with centre O . If angle ACB is a right angle , prove that angle AOB =135 degree .
    Suppose \angle BAO = x,\, \angle ABO = y.

    Then
    \angle OAY = x (congruent \triangle's OAZ, AOY)

    \angle OBX = y (congruent \triangle's OBX, OBZ)
    But
    2x + 2y = 90^o (angle sum of \triangle ABC)

    \Rightarrow x + y = 45^o

    \Rightarrow \angle AOB = 135^o (angle sum of \triangle AOB)
    Grandad
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  3. #3
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    Quote Originally Posted by Grandad View Post
    Hello thereddevilsSuppose \angle BAO = x,\, \angle ABO = y.

    Then
    \angle OAY = x (congruent \triangle's OAZ, AOY)

    \angle OBX = y (congruent \triangle's OBX, OBZ)
    But
    2x + 2y = 90^o (angle sum of \triangle ABC)

    \Rightarrow x + y = 45^o

    \Rightarrow \angle AOB = 135^o (angle sum of \triangle AOB)
    Grandad
    ohhhhhhhhhhh , thanks !!!
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