Lengths of arcs AP, BP are 20, 16 respectively, as shown. Find measure of angle AXP.
- Thread starter ssolaming
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Dr.Peterson
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First, determine the central angles for the two arcs, using the fact that AB is a diameter.
Then see this page for the appropriate theorem: https://mathbitsnotebook.com/Geometry/Circles/CRAngles.html
Then see this page for the appropriate theorem: https://mathbitsnotebook.com/Geometry/Circles/CRAngles.html
pka
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Because the line \(\displaystyle \overleftrightarrow {XP}\) is a tangent to the circle \(\displaystyle O\) so the the angle tex]m(\algleOPX)=\frac{\pi}{2}[/tex] or a right angle. Now consider \(\displaystyle angle POB\) intercepts an arc of length \(\displaystyle 16\), Can ypu use \(\displaystyle \frac{36}{180^o}=\frac{16}{m(\angle POB)}\) to show that \(\displaystyle m(\angle POB)=80^o\) so \(\displaystyle m(\angle PXB)=10^o\).