Q65.Two tangents are drawn from a point P to the circle x2 + y2 −2x −4y + 4 = 0, such that the angle between these tangents is tan−1( 125 ), where tan−1( 125 ) ∈(0, π). If the centre of the circle is denoted by C and these tangents touch the circle at points A and B, then the ratio of the areas of ΔPAB and ΔCAB is : (1) 11 : 4 (2) 9 : 4 (3) 3 : 1 (4) 2 : 1
What This Question Tests
This question combines concepts of circles and tangents with geometry to calculate ratios of areas of triangles. It requires finding the center, radius, length of tangent, and using trigonometry/geometry for areas.
Concepts Tested
Formulas Used
Equation of circle: (x-h)^2 + (y-k)^2 = r^2
Length of tangent from point P to circle
Angle between tangents
Area of triangle = 1/2 * base * height
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📋 Question Details
- Chapter
- Circles
- Topic
- Tangents to a circle & area of triangles
- Year
- 2021
- Shift
- 17 Mar Shift 2
- Q Number
- Q65
- Type
- MCQ
- NCERT Ref
- Class 11 Mathematics Ch 11: Conic Sections
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