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From an external point B, two lines BA and BC are drawn tangent to a circle, touching it at A and C respectively. E is a point on the major arc AC such that the inscribed angle AEC = 110 deg. Find the angle ABC.
- 40 deg
- 70 deg
- 110 deg
- 20 deg
Correct answer: 40 deg
Solution
Inscribed angle AEC = 110 deg subtends the minor arc AC, so the central angle AOC (reflex side) relates as: the arc not containing E has central angle = 2*110 = 220 deg, hence the central angle AOC on E's side = 360 - 220 = 140 deg. In quadrilateral OABC, OA perpendicular to BA and OC perpendicular to BC give angles 90 deg at A and C. Sum of quadrilateral angles = 360: angle ABC = 360 - 90 - 90 - 140 = 40 deg.
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