Question
Download Solution PDFThe line 3x + 4y – 24 = 0 intersects the x-axis at A and y-axis at B. Then the circumcentre of the triangle OAB where O is the origin is
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
Circumcentre: circumcenter is the point where the perpendicular bisectors of a triangle intersect.
The circumcenter of a right triangle lies exactly at the midpoint of the hypotenuse (longest side).
Calculation:
Given:
3x + 4y – 24 = 0
⇒ 3x + 4y = 24
Its x-intercept A = (8, 0) and y-intercept B = (0, 6)
Since, AOB is a right angled triangle. So, the mid-point of hypotenuse is the circumcentre.
Hence, circumcentre =
∴ circumcentre = (4, 3)
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