Q84.Consider a triangle having vertices A(−2, 3), B(1, 9) and C(3, 8). If a line L passing through the circum- centre of triangle ABC, bisects line BC, and intersects y-axis at point (0, α2 ), then the value of real number α is _______.
What This Question Tests
The question tests the ability to find the circumcentre of a triangle, the midpoint of a side, and then the equation of a line passing through these points to find its y-intercept. It combines multiple concepts from coordinate geometry.
Concepts Tested
Formulas Used
Midpoint formula: ((x1+x2)/2, (y1+y2)/2)
Slope formula: m = (y2-y1)/(x2-x1)
Equation of a line: y - y1 = m(x - x1)
Condition for perpendicular lines: m1m2 = -1
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📋 Question Details
- Chapter
- Circles
- Topic
- Circumcentre and properties of triangles
- Year
- 2021
- Shift
- 20 Jul Shift 2
- Q Number
- Q84
- Type
- Numerical
- NCERT Ref
- Class 11 Mathematics Ch 10: Straight Lines
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