Answer:
The length of edge PB is 15 cm
Step-by-step explanation:
step 1
In the triangle BOC
Find the measure of angle BOC
see the attached figure to better understand the problem
we have that
m∠CAB = 30° -----> is a inscribed angle
so
[tex]m\angle CAB=\frac{1}{2}[arc\ BC][/tex]
solve for arc BC
[tex]arc\ BC=2m\angle CAB[/tex]
substitute the given value
[tex]arc\ BC=2(30^o)=60^o[/tex]
Remember that
[tex]m\angle BOC=arc\ BC[/tex] -----> by central angle
so
[tex]m\angle BOC=60^o[/tex]
step 2
Find the length side BC
we have that
[tex]OB=OC=24\ cm[/tex] ----> the radius of the circle
so
[tex]m\angle OBC=m\angle OCB[/tex]
That means
Triangle BOC is an equilateral triangle (the measure of the interior angles is equal to 60 degrees)
therefore
[tex]BC=24\ cm[/tex]
M is the midpoint side BC
so
[tex]BM=24/2=12\ cm[/tex]
step 3
Find the length of edge PB
Applying the Pythagorean Theorem
[tex]PB^2=PM^2+BM^2[/tex]
we have
[tex]PM=9\ cm\\BM=12\ cm[/tex]
substitute
[tex]PB^2=9^2+12^2[/tex]
[tex]PB^2=225\\PB=15\ cm[/tex]
