Answer:
B. AC = 22, BC = 22, AB = 44
C. AC = 30, BC = 30, AB = 60
Step-by-step explanation:
B.
[tex] radius \: \overline {OR} \perp chord \: \overline {AB} [/tex] at C. (given)
[tex] \therefore AC = BC[/tex] (perpendicular dropped from the center of the circle to the chord bisects the chord)
[tex] \therefore 2x - 6 = x + 8[/tex]
[tex] \therefore 2x - x= 6 + 8[/tex]
[tex] \therefore x= 14[/tex]
[tex] AC = 2x-6=2(14)-6=28-6= 22[/tex]
[tex] BC= x + 8=14 + 8= 22[/tex]
AB = AC + BC = 22 + 22 = 44
C.
[tex] radius \: \overline {OR} \perp chord \: \overline {AB} [/tex] at C. (given)
[tex] \therefore BC = AC[/tex] (perpendicular dropped from the center of the circle to the chord bisects the chord)
[tex] \therefore 7x-5=4x+10 [/tex]
[tex] \therefore 7x - 4x= 5 + 10[/tex]
[tex] \therefore 3x= 15[/tex]
[tex] \therefore x= \frac{15}{3}[/tex]
[tex] \therefore x= 5[/tex]
[tex] AC = 4x+10=4(5)+10=20+10= 30[/tex]
[tex] BC= 7x - 5=7(5)-5=35-5= 30[/tex]
AB = AC + BC = 30 + 30 = 60
