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Chord, Tangent and the Circle

The Intersection of a Tangent and Chord

Picture of chord and tangent, angle and arc

    The Theorem: An Angle formed by a chord and a tangent that intersect on a circle is half the measure of the intercepted arc

    Look at the picture on the left

    • arc abc

      This means that the measure of arc ABC (the purple portion of the circle itself) is twice the measure of angle C.

Practice Problems


Angles formed by chords and tangents

Use the theorem above to find the measure of angle formed by the intersection of the tangent that intersects chord AC. Picture of angle formed by tangent and chord


 Measure of angle  

 

What is the ?

Answer


For measaure of arc abc (the measure of arc ABC) to equal ¾ the total measure of the circle's circumference, what must be the value of X ?
Answer
Look at Circle 1 and Circlce 2 below. In only one of the two circles does a tangent interesect with a chord. Which circle is it?
Answer