In the figure, line segment AB is tangent to circle O at point A, secant BD intersects circle O at points C and D, the measure of arc AC = 70°, and the measure of arc CD = 110°. 70 /110" What is the measure of angle ABC? О А. 55° о В. 70° о С. 40° D. 20°

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Chapter7: Triangles
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In the figure, line segment AB is tangent to circle O at point A, secant BD intersects circle O at points C and D, the measure
of arc AC = 70°, and the measure of arc CD = 110°.
70
110
What is the measure of angle ABC?
О А. 55°
о В. 70°
О С. 40°
O D. 20°
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Transcribed Image Text:In the figure, line segment AB is tangent to circle O at point A, secant BD intersects circle O at points C and D, the measure of arc AC = 70°, and the measure of arc CD = 110°. 70 110 What is the measure of angle ABC? О А. 55° о В. 70° О С. 40° O D. 20° Sign out DVO
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BAO = 90°      [Property of tangant to a circle]AOC =70°       [ Given]COD =110°      AOC+COD=70°+110°=180°So, line AO+OD is a straight line AD which passes through the centre of the circle.Now, OC=OD [Radius of the circle]Therefore, OCD is an isosceles triangle.Thus, OCD=ODCLet both the angles be x.Therefore, OCD+ODC+DOC=180°x+x+DOC =180°2x = 180°-DOC 2x   = 180°-110°   x   =   702   x   =    35°

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