ABCD is a trapezium where AD|| BC. The diagonal AC and BD

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ABCD is a trapezium where AD|| BC. The diagonal AC and BD intersect each other at the point O. If AO = 3, CO = x – 3, BO = 3x – 19 and DO = x – 5, the value of x is

1. – 8, 9
2. 8, – 9
3. – 8, – 9
4. 8, 9

Correct Option: D

As per the given in question , we draw a figure trapezium ABCD

Given that , AO = 3, CO = x – 3, BO = 3x – 19 and DO = x – 5,
We have , AO × BO = OD × OC
⇒ 3 (3x – 19) = (x – 5) (x – 3)
⇒ 9x – 57 = x² – 8x + 15
⇒ x² – 17x + 72 = 0
⇒ x² – 9x – 8x + 72 = 0
⇒ x (x – 9) – 8 (x – 9) = 0
⇒ (x – 8) (x – 9) = 0
⇒ x = 8 or 9