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Math Help - Proving Congruence

  1. #1
    Member GAdams's Avatar
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    Proving Congruence

    File attached. I'm not too sure how to do this, here's what I have so far:

    BP = PC (tangents that cross coming from a circle) [side]

    angle ACX = angle ABC (alternate segments)

    angle YBA = angle ACD (alternate angles)

    Therefore, angle ABC = ACB
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    A riddle wrapped in an enigma
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    Quote Originally Posted by GAdams View Post
    File attached. I'm not too sure how to do this, here's what I have so far:

    BP = PC (tangents that cross coming from a circle) [side]

    angle ACX = angle ABC (alternate segments)

    angle YBA = angle ACD (alternate angles)

    Therefore, angle ABC = ACB
    Hi GAdams,

    Prove \triangle APB \cong \triangle APC

    \angle ABC \cong \angle ACB - Given

    \overline{PB} \ \ and \ \ \overline{PC} are tangent to the circle - Given


    \overline{AB} \cong \overline{AC} - If two angles of a triangle are congruent, then the sides opposite these angles are congruent.

    \overline{BP} \cong \overline{CP} - If two segments from the same exterior point are tangent to a circle, then they are congruent.

    \overline{AP} \cong \overline {AP} - Reflexive property of congruence.

    \triangle APB \cong \triangle APC - SSS Postulate
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  3. #3
    Member GAdams's Avatar
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    than you!
    Not sure how to find angle ABC...

    I can see that angle BPA and angle CPA are the same
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    A riddle wrapped in an enigma
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    Quote Originally Posted by GAdams View Post
    than you!
    Not sure how to find angle ABC...

    I can see that angle BPA and angle CPA are the same
    m \angle BPA=10

    \triangle BPC is isosceles.

    m \angle PBC=m \angle PCB=80

    m \widehat{BC}=160

    m \widehat{BAC}=200

    m \widehat {AB}=m \widehat {AC}=100

    m \angle ABC=\frac{1}{2} m \widehat{AB}=50
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