In the digram, O is the centre of the circle and EG and EF are both tangents to the circle at D and A respectively. Given that ∡AOC = 125° and ∡DCO = 27°, find
(i) ∡ABC,
(ii) ∡DAE,
(iii) ∡AED.
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Answer:
(i) ∡ADC = 125° / 2 = 62.5° (angle at centre = 2 * angle at circumference)
∡ABC = 180° - ∡ADC = 180° - 62.5°
∡ABC = 117.5° (opposite angles in a cyclic quad add up to 180°)
(ii) reflex angle AOC = 360° - 125° = 235°
∡OAD = 360° - 235° - 27° - 62.5°(∡ADC) = 35.5° (angles in a quadrilateral add up to 360°)
∡DAE = ∡OAE - ∡OAD = 90° - 35.5° = 54.5°
(iii) ∡ADE = ∡DAE = 54.5° (isosceles triangle)
∡AED = 180° -54.5° -54.5° = 71° (angles in a triangle add up to 180° )
