A quadrilateral ABCD is inscribed in a circle such that AB : CD = 2 : 1 and BC : AD = 5 : 4. If AC and BD intersect at the point E, then AE : CE equals
Explanation:
∠DAC = ∠DBC [angle subtended in same segment by same chord are equal] Similarly, ∠ADB = ∠ACB ∠CDB = ∠CAB ∠ACD = ∠ABD
∆AED is similar to ∆BEC [∠DAC = ∠DBC and ∠ADB = ∠ACB] ∴ EDEC = ADBC = 45 ...(1)
∆AEB is similar to ∆DEC [∠CDB = ∠CAB and ∠ACD = ∠ABD] ∴ AEED = ABCD = 21 ...(2)
(1) × (2) ⇒EDEC×AEED = 45×21 = 85
Hence, option (d).
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