Question

What is the area and circumference of circle p? explain how you calculated this answer. if the arc measure of arc cod is 100∘ and the arc measure of arc bsa is 60∘, what is the angle measure of angle crb? explain how you calculated this answer?

Answer 1

the picture in the attached figure

step 1

find RD

we know that

When two chords intersect each other inside a circle, the products of their segments are equal (Intersecting Chord Theorem)

so

AR*RC=RB*RD-------> solve for RD

RD=(AR*RC)/RB-----> RD=(4*4.5)/3------> RD=6

RB+RD-----> is equal to the diameter of the circle

so

diameter=3+6------> diameter=9 units

radius=diameter/2-------> radius=9/2-----> radius=4.5 units

step 2

find the area of the circle p

Area of the circle=pi*r²--------> Area=pi*4.5²

Area=20.25*pi units²--------> Area=63.62 units²

step 3

find the circumference of the circle p

circumference=2*pi*r------> 2*pi*4.5

circumference=9*pi units-------> circumference=28.27 units

step 4

we know that

The measure of the interior angle is the half-summit of the arcs that comprise it and its opposite.

so

∠CRD=(1/2)*[arc COD+arc BSA]-----> ∠CRD=(1/2)*[100°+60°]----> 80°

∠CRD=80°

∠CRD+∠CRB=180°-------> by supplementary angles

so

∠CRB=180°-∠CRD----------> ∠CRB=180°80°-----> ∠CRB=100°