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Draw ΔABC with AB = 5 cm, ∠A = 70° and ∠B = 60°. Draw the circumcircle of ΔABC. Is the centre inside or outside the triangle?
The constructed triangle is an acute-angled triangle. In such triangles, the perpendicular bisectors of all three sides intersect at a point inside the triangle. This point is called the circumcentre. A circle drawn with this point as the centre passes through all three vertices of the triangle. HenRead more
The constructed triangle is an acute-angled triangle. In such triangles, the perpendicular bisectors of all three sides intersect at a point inside the triangle. This point is called the circumcentre. A circle drawn with this point as the centre passes through all three vertices of the triangle. Hence, the circumcentre of the circumcircle lies inside the triangle.
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 lessDraw ΔABC with AB = 5 cm, ∠A = 100°, AC = 4 cm. Draw the circumcircle of ΔABC. Is the centre inside or outside the triangle?
The given construction forms an obtuse-angled triangle. In an obtuse-angled triangle, the perpendicular bisectors of the sides intersect at a point outside the triangle. This point is called the circumcentre. A circle drawn with this point as the centre passes through all three vertices of the trianRead more
The given construction forms an obtuse-angled triangle. In an obtuse-angled triangle, the perpendicular bisectors of the sides intersect at a point outside the triangle. This point is called the circumcentre. A circle drawn with this point as the centre passes through all three vertices of the triangle. Hence, the circumcentre lies outside the triangle.
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 lessDraw ΔABC, with AB = 6 cm, BC = 7 cm and CA = 7 cm. Draw the circumcircle of ΔABC. Let the circumcentre be O. Measure OA, OB, OC.
The circumcentre is the point where the perpendicular bisectors of the triangle meet. It is equally distant from all three vertices. Therefore, the lengths of OA, OB and OC are equal. When measured with a ruler, the three distances should be the same. Any slight variation is usually caused by smallRead more
The circumcentre is the point where the perpendicular bisectors of the triangle meet. It is equally distant from all three vertices. Therefore, the lengths of OA, OB and OC are equal. When measured with a ruler, the three distances should be the same. Any slight variation is usually caused by small construction or measurement errors.
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 lessWhat is the least possible radius of a circle through two points A and B?
Infinitely many circles can pass through two given points. Among them, the smallest circle is formed when the two points become the endpoints of the diameter. In this case, the centre lies at the midpoint of the line segment joining the points. Therefore, the least possible radius is equal to half tRead more
Infinitely many circles can pass through two given points. Among them, the smallest circle is formed when the two points become the endpoints of the diameter. In this case, the centre lies at the midpoint of the line segment joining the points. Therefore, the least possible radius is equal to half the distance between the two given 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 lessA, 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 less