ESIC Nursing Officer -2019 (Shift -1)
Non Nursing Subjects
Medium
In the following figure, if PM overline AT is perpendicular, PT = 10 and PM =8 vec 6 then the value of AT is:
Appeared in: ESIC Nursing Officer -2019 (Shift -1)
Explanation
- The problem requires finding the length of the chord AB using the given radius and the perpendicular distance from the center to the chord.
- A right-angled triangle (ΔPMB) is formed by the radius (PB), the perpendicular (PM), and half the chord (MB).
- Applying the Pythagorean theorem (hypotenuse² = base² + perpendicular²), we can find the length of MB.
- The theorem states that a perpendicular drawn from the center of a circle to a chord bisects the chord. Therefore, the full length of the chord AB is twice the length of MB.
Why Other Options Were Wrong
- Option A: This value (36) is the square of the length of half the chord (MB² = 6² = 36). It is an intermediate calculation step, not the final length of the chord.
- Option B: This value (10) is the length of the radius (PB) given in the problem. The chord's length is a different measurement.
- Option C: This value (6) is the length of half the chord (MB), which is correctly calculated using the Pythagorean theorem. However, the question asks for the length of the entire chord AB.
Related Visual
- Visual 1: Diagram illustrating the relationship between the radius, a chord, and the perpendicular from the center, highlighting the right-angled triangle used in the Pythagorean theorem.
Clinical Relevance
- Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Application of the Pythagorean theorem to find the length of a chord in a circle as background academic context rather than a clinical decision trigger.
- This is a question from the non-nursing subject of Mathematics (Geometry).
- It tests basic geometric principles and problem-solving skills, which are part of the general aptitude section of some nursing examinations.
- There is no direct clinical relevance to this question.
How to Approach the Question
- Analyze the image to understand the geometric setup. Identify the given lengths: radius (PB = 10) and the perpendicular from the center to the chord (PM = 8).
- Recognize that the radius, the perpendicular, and half the chord form a right-angled triangle (ΔPMB).
- Apply the Pythagorean theorem: PB² = PM² + MB².
- Substitute the known values and solve for the unknown side MB: 10² = 8² + MB², which gives MB = 6.
- Recall the property of circles that a perpendicular from the center bisects the chord (AB = 2 * MB).
- Calculate the full length of the chord: AB = 2 * 6 = 12.
Concept Tested & Keywords
- Concept Tested: Application of the Pythagorean theorem to find the length of a chord in a circle.
- Stem keywords: circle, chord, perpendicular, radius, Pythagorean theorem
- Lead-in keywords: value of
Question ID
Qx_6tPP4wcsK8bk0M6c1zj
Practise the full ESIC Nursing Officer -2019 (Shift -1)
Attempt every question from this paper in a timed mock, then review the full solution for each one.
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