Question

a. What is the area and circumference of circle P? Explain how you calculated this answer. b. If the arc measure of arc COD is 100 degrees and the arc measure of arc BSA is 60 degrees, what is the angle measure of angle CRB ? Explain how you calculated this answer.

Answer 1

a) 9*π or approx 28.26

b) ∡CRB=100°

Explanation:

As known for secants crossing each other inside the circle is coorect the following:

BR*RD=AR*RC

=> 3*RD=4*4.5

RD=6

The diameter of the circle with center P is BD=BR+RD=3+6=9

So the radius of the circle is D/2=9/2=4.5

As known the circumference of any circle can be calculated as

C=2*π*r , where r is the circle's radius

So C=2*4.5*π=9*π= approx 3.14*9=28.26

b) ∡CRB=∡ARD= (arcBC+arcAD), where arcBC and arcAD smaller arcs

BD is the circle's diameter, so arc BD=180°

So arcBC=180°-arcCOD=180°-100°=80°

Similarly arcBD=180°

arcAD=180°-arcBSA=180°-60°=120°

∡CRB= (80°+120°)/2=100°