Questions and Answers
In a circle of radius 5 cm, an arc subtends an angle of 60 degrees at the centre. Find the length of the arc.
Use the formula, length of arc = (θ/360) × 2 × π × r, θ in degrees.
Prove that the points $(a, b + c), (a, b), (a + c, b)$ and $(a + c, b + c)$ are the vertices of a parallelogram.
Draw a diagram and show that opposite sides are equal using distance formula.
Prove that $(1 + cot A)/ (cosec A) = sin A$.
Use trigonometric identities and simplify the given expression.
Find the value of $sin^{-1} (1/2) + cos^{-1} (1/2)$.
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Find the coordinates of the point which divides the line segment joining the points $(2, 4)$ and $(8, 10)$ in the ratio 3:2.
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Study Notes
Properties of Shapes
- The points $(a, b + c), (a, b), (a + c, b)$ and $(a + c, b + c)$ are the vertices of a parallelogram.
Circle Properties
- In a circle of radius 5 cm, an arc subtends an angle of 60 degrees at the centre, implying the arc length is a portion of the circle's circumference.
Trigonometric Identities
- $(1 + cot A)/ (cosec A) = sin A$ is a trigonometric identity.
Trigonometric Functions
- The value of $sin^{-1} (1/2) + cos^{-1} (1/2)$ can be found by evaluating the inverse sine and cosine of 1/2.
Coordinate Geometry
- The coordinates of the point dividing the line segment joining $(2, 4)$ and $(8, 10)$ in the ratio 3:2 can be found using the section formula.
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Description
Test your understanding of the first four chapters of class 10 mathematics with these 50 marks questions covering topics such as coordinate geometry, circle, and trigonometry.
