SOLUTION: Prove: If two circles are tangent internally at point P and chord PA of the larger circle intersects the smaller circle at B, then the measure of arc PA is equal to the measure of

Algebra ->  Geometry-proofs -> SOLUTION: Prove: If two circles are tangent internally at point P and chord PA of the larger circle intersects the smaller circle at B, then the measure of arc PA is equal to the measure of       Log On


   

Question 1140344: Prove: If two circles are tangent internally at point P and chord PA of the larger circle intersects the smaller circle at B, then the measure of arc PA is equal to the measure of arc PB.
Answer by ikleyn(52787) About Me  (Show Source):
You can put this solution on YOUR website!
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The measure of the angle between a chord and a tangent line to a circle at the endpoint of the chord
is half the measure of the arc stretched by the chord.


        For this statement, see the lesson
            - The angle between a chord and a tangent line to a circle,
        in this site.


Since the angle between the tangent line and the chord is the same for both circles,
the two arcs have equal angular measures.

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There is this free of charge online textbook on Geometry
    GEOMETRY - YOUR ONLINE TEXTBOOK
in this site.

The referred lesson is the part of this online textbook under the topic  "Properties of circles, inscribed angles, chords, secants and tangents ".


Save the link to this online textbook together with its description

Free of charge online textbook in GEOMETRY
https://www.algebra.com/algebra/homework/Triangles/GEOMETRY-your-online-textbook.lesson

to your archive and use it when it is needed.