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      Question

      In △ ABC, AB = AC. A circle drawn through B touches AC

      at D and intersect AB at P. If D is the midpoint of AC and AP = 2.5 cm, then AB is equal to:
      A 12.5 cm Correct Answer Incorrect Answer
      B 10 cm Correct Answer Incorrect Answer
      C 9 cm Correct Answer Incorrect Answer
      D 7.5 cm Correct Answer Incorrect Answer

      Solution

      AB = AC AC = 2 AD As we know, AD = AP × AB ⇒ AD = 2.5 × AC ⇒ AD = 2.5 × 2AD AD = 5 cm ⇒ AC = 2 × 5 = 10 cm ∴ AB = AC = 10 cm

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