Mathematics
In the figure (ii) given below, AC is a diameter of the given circle and ∠BCD = 75°. Calculate the size of
(i) ∠ABC
(ii) ∠EAF
Circles
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Answer
(i) From figure,
∠ABC = 90° (∵ angle in semicircle is equal to 90°)
Hence, the value of ∠ABC = 90°.
(ii) Since opposite angles sum is 180° in cyclic quadrilateral
⇒ ∠BAD + ∠BCD = 180°
⇒ ∠BAD + 75° = 180°
⇒ ∠BAD = 180° - 75°
⇒ ∠BAD = 105°.
From figure,
∠EAF = ∠BAD = 105°.
Hence, the value of ∠BAD = 105°.
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