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In the given figure, CD and AB are diameters of circle and AB and CD are perpendicular to each other. QL and SR are perpendiculars to AB and CD respectively. Radius of circle is 5 cm, PB ∶ PA = 2 ∶ 3 and CN ∶ ND = 2 : 3. What is the length (in cm) of SM?
  • a)
    [(5√3) - 3]
  • b)
    [(4√3) - 2]
  • c)
    [(2√5) - 1]
  • d)
    [(2√6) - 1]
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
In the given figure, CD and AB are diameters of circle and AB and CD a...

Since PA ∶ PB = 3 ∶ 2 and AB is diameter which is equal to 10 cm,
⇒ PA = 3/5 × 10 = 6 cm and PB = 10 - 6 = 4 cm
Since AO is the radius of the circle,
∴ OP = 6 - 5 = 1 cm
In the same way,
ND = 6 cm and NC = 4 cm
∴ NO = 6 - 5 = 1 cm
Now applying Pythagoras theorem in ΔOSN,
⇒ OS2 = NS2 + NO2
Since OS is the radius of the circle, OS = 5 cm
⇒ 25 = NS2 + 1
⇒ NS = 2√6
∴ SM = (2√6 - 1) cm
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In the given figure, CD and AB are diameters of circle and AB and CD are perpendicular to each other. QL and SR are perpendiculars to AB and CD respectively. Radius of circle is 5 cm, PB PA = 2 3 and CN ND = 2 : 3. What is the length (in cm) of SM?a)[(5√3) - 3]b)[(4√3) - 2]c)[(2√5) - 1]d)[(2√6) - 1]Correct answer is option 'D'. Can you explain this answer?
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In the given figure, CD and AB are diameters of circle and AB and CD are perpendicular to each other. QL and SR are perpendiculars to AB and CD respectively. Radius of circle is 5 cm, PB PA = 2 3 and CN ND = 2 : 3. What is the length (in cm) of SM?a)[(5√3) - 3]b)[(4√3) - 2]c)[(2√5) - 1]d)[(2√6) - 1]Correct answer is option 'D'. Can you explain this answer? for UGC NET 2024 is part of UGC NET preparation. The Question and answers have been prepared according to the UGC NET exam syllabus. Information about In the given figure, CD and AB are diameters of circle and AB and CD are perpendicular to each other. QL and SR are perpendiculars to AB and CD respectively. Radius of circle is 5 cm, PB PA = 2 3 and CN ND = 2 : 3. What is the length (in cm) of SM?a)[(5√3) - 3]b)[(4√3) - 2]c)[(2√5) - 1]d)[(2√6) - 1]Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for UGC NET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In the given figure, CD and AB are diameters of circle and AB and CD are perpendicular to each other. QL and SR are perpendiculars to AB and CD respectively. Radius of circle is 5 cm, PB PA = 2 3 and CN ND = 2 : 3. What is the length (in cm) of SM?a)[(5√3) - 3]b)[(4√3) - 2]c)[(2√5) - 1]d)[(2√6) - 1]Correct answer is option 'D'. Can you explain this answer?.
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