Question

11. In the figure PA and PB are tangents.
If angle APB=70', what is the measure of angle ACB ?​

Answer 1

Answer:

< AOB + < APB = 180

=> < AOB + 70 = 180 => < AOB = 180 - 70

=> < AOB = 110

We know that angle subtended by an arc at the center is double the angle at the remaining part of the circle

so , < AOB = 2 < ACB

=> 110 = 2 < ACB

=> < ACB = 110 / 2 = 55

Answer 2

CENTRAL ANGLE IS TWICE ANY INSCRIBED ANGLE SUBTENDED BY THE SAME ARC.

Step-by-step explanation:

• Tangents make angle 90 ,therefore angle OBP=90 and OAP=90.

• we know that in qaudrilateral summation of all angles is 360.
• let the angle BOA=X.

• BOA+OAP+APB+PBO=360

• X+90+90+70=360

• X=110
• central angle is twice any inscribed angle subtended by the same arc.

• angle ACB=BOA/2

                  =X/2

                  =110/2

                  =55

so the final answer is 55 degree.