A
Р
(ii) In the figure, m(arc APC)=110° then find
the measure of ZABC
(a) 55°
(b) 110°
(c) 50°
(d) 60°
C С
B
Answers
Given : m(arc APC) =110°
To Find : measure of angle ABC
Solution:
As figure is missing :
Considering few cases
P & B are points in same arc segments
then m(arc ABC) = m(arc APC)
=> m(arc ABC) = 110°
P & B are points in different arc segments
then m(arc ABC) + m(arc APC) = 180° ( opposite angles of cyclic quadrilateral )
m(arc ABC) + 110° = 180°
=> m(arc ABC) = 70°
P is at center and B is at remaining circle
=> m(arc ABC) = (1/2) m(arc ABPC)
=> m(arc ABC) = (1/2)110°
=> m(arc ABC) = 55°
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Answer:
the anwer for this question is (A) 55