Question
Download Solution PDFA, B, C are three points such that AB = 11 cm, BC = 13 cm and AC = 24 cm. Number of circles passing through the points A, B, C is:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
A, B, C are three points such that AB = 11 cm, BC = 13 cm, and AC = 24 cm.
Formula used:
For three points to lie on a circle, the sum of the lengths of any two sides must be greater than the third side (Triangle Inequality Theorem).
Calculation:
Check triangle inequality for AB, BC, and AC:
AB + BC > AC
11 + 13 > 24
24 = 24 (Not greater)
BC + AC > AB
13 + 24 > 11
37 > 11 (True)
AC + AB > BC
24 + 11 > 13
35 > 13 (True)
Since AB + BC is not greater than AC, the points A, B, C do not form a triangle and hence cannot lie on the same circle.
∴ The correct answer is option 1.
Last updated on May 28, 2025
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