যদি দুটি জ্যা AB এবং CD, O বিন্দুতে ছেদ করে এবং AO = (9x – 2) সেমি, BO = (2x + 2) সেমি, CO = 4x সেমি এবং DO = (7x – 2) সেমি হয়, তাহলে, AO (x > 1) এর মান নির্ণয় করুন।

  1. 12 সেমি
  2. 14 সেমি
  3. 16 সেমি
  4. 18 সেমি

Answer (Detailed Solution Below)

Option 3 : 16 সেমি
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Detailed Solution

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আমরা জানি যে,

AO × OB = OC × OD

⇒ (9x – 2) × (2x + 2) = (4x) × (7x – 2)

⇒ 18x2 – 4x + 18x – 4 = 28x2 – 8x

⇒ 10x2 – 22x + 4 = 0

⇒ 10x2 – 20x – 2x + 4 = 0

⇒ 10x(x – 2) – 2(x – 2) = 0

⇒ (x – 2)(10x – 2)  = 0

⇒ x = 2 বা x = 0.2

⇒ x = 2

AO = (9x – 2) = (18 – 2) = 16 সেমি

∴ AO এর মান হল 16 সেমি

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