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A, B, C, D and E are points on a circle. Point C is due north of point D and point E is due west of point D. ∠CAB = 27°. The angle of elevation of point B from point E is 87°. The angle of elevation of point B from point D is

(a) 60° 

(b) 33° 

(c) 63° 

(d) 24°

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Answer : (c) 63º 

The required angle is ∠BDE. C is north of D and E is west of  D 

⇒ ∠CDE = 90° ⇒ EC is the diameter of the circle

(∵ Angle in a semicircle is a rt. ∠) 

∴ ∠EBC = 90° (Angle in a semicircle) 

∠BEC = ∠BAC = 27° (Angle in the same segment are equal) 

∴ In ∆ EBC, ∠ECB = 180° – (∠EBC + ∠BEC) 

= 180° – (90° + 27°) = 63°. (Angle sum property of a ∆) 

⇒ ∠BDE = ∠BCE = 63° (Angles in the same segment are equal)

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