In an isosceles triangle, the altitude from the vertex bisects the base. The perpendicular bisector of a chord passes through the centre of the circle. Therefore, the altitude passes through the centre.
An isosceles triangle ABC is inscribed in a circle, with AB = AC. Show that the altitude from A to BC passes through the centre of the circle.
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Since AB = AC, triangle ABC is isosceles. The altitude drawn from A to BC also bisects BC. As BC is a chord of the circumcircle, its perpendicular bisector always passes through the centre of the circle. Therefore, the altitude from A to BC passes through the centre of the circle.
For more NCERT Solutions for Class 9 Maths Ganita Manjari Chapter 5 I’m Up and Down and Round and Round (2026-27):
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