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A, B and C are three collinear points. Can you find a point P such that PA = PB = PC? What can you say about the perpendicular bisectors of AB and BC? Draw and check. Can you show that for three collinear points A, B and C, the perpendicular bisector of AB and BC are parallel? Is it possible for a circle to pass through collinear points? Can you draw a line that cuts a given circle in three distinct points?
No point can be equally distant from three collinear points. The perpendicular bisectors of AB and BC remain parallel, so they never meet to form a circumcentre. Without a common circumcentre, a circle cannot pass through all three collinear points. Also, a straight line can intersect a circle at aRead more
No point can be equally distant from three collinear points. The perpendicular bisectors of AB and BC remain parallel, so they never meet to form a circumcentre. Without a common circumcentre, a circle cannot pass through all three collinear points. Also, a straight line can intersect a circle at a maximum of two distinct points, never at three distinct points.
For more NCERT Solutions for Class 9 Maths Ganita Manjari Chapter 5 I’m Up and Down and Round and Round (2026-27):
https://www.tiwariacademy.com/ncert-solutions/class-9/maths/ganita-manjari-chapter-5/
See lessThe circumcircle of a given ΔABC is drawn. Can there be other triangles congruent to ΔABC that share the same circumcircle?
Yes, it is possible to construct other triangles congruent to the given triangle on the same circumcircle. These triangles have identical side lengths and angles but occupy different positions on the circle. Although their orientation changes, they remain congruent and share the same circumcircle.Read more
Yes, it is possible to construct other triangles congruent to the given triangle on the same circumcircle. These triangles have identical side lengths and angles but occupy different positions on the circle. Although their orientation changes, they remain congruent and share the same circumcircle.
For more NCERT Solutions for Class 9 Maths Ganita Manjari Chapter 5 I’m Up and Down and Round and Round (2026-27):
https://www.tiwariacademy.com/ncert-solutions/class-9/maths/ganita-manjari-chapter-5/
See lessFind the value of x cube – 8y cube – 36xy – 216, when x = 2y + 6
We analyze the given conditional equation by moving terms to one side, which gives the simplified statement x - 2y - 6 = 0. Now, we rewrite the main polynomial expression using these exact bases, formatting it as x cube + (-2y) cube + (-6) cube minus 3 times x times (-2y) times (-6). According to alRead more
We analyze the given conditional equation by moving terms to one side, which gives the simplified statement x – 2y – 6 = 0. Now, we rewrite the main polynomial expression using these exact bases, formatting it as x cube + (-2y) cube + (-6) cube minus 3 times x times (-2y) times (-6). According to algebraic conditions, when the sum of three base terms is equal to zero, the sum of their individual cubes minus three times their product automatically equals zero. Thus, the answer is 0.
For more NCERT Solutions for Class 9 Maths Ganita Manjari Chapter 4 Exploring Algebraic Identities (2026-27):
https://www.tiwariacademy.com/ncert-solutions/class-9/maths/ganita-manjari-chapter-4/
See lessFind the value of x cube + y cube – 12xy + 64 when x + y = -4
We rearrange the given polynomial expression into the standard conditional cubic identity template. We can rewrite the mathematical statement as x cube + y cube + (4) cube minus 3 times x times y times 4. This matches the identity where the three components are x, y and 4. The identity states that iRead more
We rearrange the given polynomial expression into the standard conditional cubic identity template. We can rewrite the mathematical statement as x cube + y cube + (4) cube minus 3 times x times y times 4. This matches the identity where the three components are x, y and 4. The identity states that if the sum of these three numbers equals zero, the total expression equals zero. Since x + y = -4, the sum x + y + 4 equals zero, making the value 0.
For more NCERT Solutions for Class 9 Maths Ganita Manjari Chapter 4 Exploring Algebraic Identities (2026-27):
https://www.tiwariacademy.com/ncert-solutions/class-9/maths/ganita-manjari-chapter-4/
See lessBy factoring the expression, check that n cube – n is always divisible by 6 for all natural numbers n.
We begin by completely factoring the given cubic expression. Taking out the common term n gives n(n square - 1), which further opens up into the three-part continuous variable expression (n - 1)(n)(n + 1). This product represents three consecutive natural numbers. In any sequence of three consecutivRead more
We begin by completely factoring the given cubic expression. Taking out the common term n gives n(n square – 1), which further opens up into the three-part continuous variable expression (n – 1)(n)(n + 1). This product represents three consecutive natural numbers. In any sequence of three consecutive numbers, at least one number must be even (divisible by 2) and exactly one must be a multiple of 3. Their product is therefore always divisible by 2 times 3, which equals 6.
For more NCERT Solutions for Class 9 Maths Ganita Manjari Chapter 4 Exploring Algebraic Identities (2026-27):
https://www.tiwariacademy.com/ncert-solutions/class-9/maths/ganita-manjari-chapter-4/
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