Mind Warmups-9
Geometry
Level
3
In the figure above (not drawn to scale). A,B and C are three points on a circle with centre O. The chord BA is extended to a point T such that CT becomes a tangent to the circle at point C. if angle ATC = 30° and ACT = 50°, then the angle BOA is..
not possible to determine
100
80
150
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1 solution
Draw radius OC.
Angle BAC is the sum of angles ACT and ATC,i.e 50 + 30 = 80.
Angle OCT is 90 degrees.
Angle OCA becomes 40 degrees.
Angles OCA and OAC are equal to 40 degrees.
Angle OAB = angle BAC- angle OAC,i.e 80 - 40 = 40.
Angle OBA = angle OAB = 40.
Angle BOA = 180 - (angle OBA+ angle OAB). = 180 - 80 = 100