Class 9 maths chapter 5 circle day 4 new ncert theorem and exercise 5.3

This video (Day 4 of Class 9 Maths, Chapter 5: Circles) explains the relationship between the center of a circle, chords, and perpendicular bisectors. The key topics covered include: Fundamental Concepts: The narrator defines the midpoint of a chord as the point that divides it into two equal parts (0:18) and explains that a perpendicular bisector is a line from the center that meets the chord at 90 degrees and bisects it (0:41). Theorem 4: This theorem states that a line segment joining the center of a circle to the midpoint of a chord is perpendicular to that chord (1:07). The proof uses triangle congruency (SSS) to show that the angles formed are equal and must be 90 degrees (3:10 - 5:15). Exercise 5.3 (Question 1): The video proves the converse: if a perpendicular is drawn from the center to a chord, it bisects the chord (5:50). This is proven using RHS congruency (7:32 - 8:45). Exercise 5.3 (Question 2): The narrator demonstrates that an altitude from the vertex of an isosceles triangle inscribed in a circle must pass through the circle's center (9:02 - 14:27). This involves proving the triangle is congruent and showing that the altitude and the perpendicular line from the center must coincide (10:23 - 14:12).