Question

Select the correct answer. And are tangent to circle C and circle F. The points of tangency are A, B, D, and E. If m∠DFE = 140°, what is m∠ACB? A. 160° B. 140° C. 120° D. 110°

Answer 1

Answer: 140°

Steps:

1) We know that, Sum of angles subtended at the centre and point of contact by tangents down from an external point is supplementary (180°).

=> /GFE + / DGE = 180°

=> 140° + /DGE = 180°

=> /DGE = 40°

3) Again Applying above Theorem,

=> /AGB + / ACB = 180°

=> 40° + /ACB = 180°

=> /ACB = 140° .

Hence, Angle ACB = 140°