11.02 Lines tangent to a circle
Interactive practice questions
In the figure below, $AC$AC is tangent to both circles.
Two circles are positioned side by side, touching at a single point $B$B. The larger circle on the left has center labeled $O$O. The smaller circle on the right has center labeled $P$P. Radius $OB$OB connects the center $O$O to tangent point $B$B. Radius $BP$BP connects the center $P$P to tangent point $B$B. A vertical line $AC$AC passes through point $B$B, and is tangent to both circles.
Show that $\angle OBP$∠OBP is a straight angle.
Therefore what can we say about points $O$O, $B$B and $P$P?
They form a triangle.
They are collinear.
In the diagram, $AC$AC is a tangent to the circle with center $O$O. What is the measure of $x$x?
In the figure, $\overline{BA}$BA is a tangent to the circle.
Determine the value of $a$a in the following diagram, showing all steps of working.