Lemma 2.4.7 (page 93) talks about "intercepted arcs." Try to
give a precise description of these arcs (without referring to pictures).
Show that if two chords of a circle intersect at a point P inside the
circle, then the measure of ÐP
is the average of the measures of the two intercepted arcs. (Note that there
are four angles that could be interpreted as "ÐP";
which one(s) are we talking about here?)
Let g
be a circle and ÐA
an angle whose vertex is outside g
and whose sides are tangent to g.
Find a relationship between the measure of ÐA
and the measure of the minor arc (just the minor arc, not the major arc!) of
g
"intercepted" by ÐA.