Class 9th maths ch 5 Ex 5.4 based on new NCERT book ganita manjari

Theorem 6 (Equal Chords and Distance): The instructor explains that if two chords of a circle have equal lengths, they are at an equal distance from the center. The proof involves constructing triangles (OBE and ODF) and using congruence (RHS property) to demonstrate that the distances (OE and OF) are equal (0:23 - 6:27). Question 1: Re-proves the property from Theorem 6 using the Pythagorean theorem (referred to as Budhayana-Pythagoras theorem), demonstrating the equality of distances from the center (6:32 - 13:17). Question 2: Explores the converse: if two chords are at an equal distance from the center, then the chords themselves must be equal in length. This is proved through triangle congruence (13:21 - 17:26). Question 3: Re-proves the property from Question 2 using the Pythagorean theorem, showing how equal distances from the center result in equal chord lengths (17:27 - 23:05).