Question

help in solving 9 part

Answer 1

Drop the perpendiculars to the chords. We know that perpendicular from the centre bisects the chord.

Hence, for chord of 6cm,

3² + h² = r²

Where, h is the height of the perpendicular, r is the radius.


Now for chord of 8cm, the height would be h - 7 as they are 7 cm apart (refer the figure)

=> 4² + (h - 7)² = r²

So equate the two equations

=> 4² + (h - 7)² = 3² + h²

=> 16 + h² + 49 - 14h = 9 + h²

=> 16 - 9 + h² - h² + 49 = 14h

=> 56 = 14h

=> h = 56/14

=> h = 4


Now since, h < 7

=> chords are not on the same side.

Anyway, the answer would still come right as the square of a number is always positive.

So, r² = 3² + h²

=> r² = 9 + 4²

=> r² = 25

=> r = 5 cm


Hope you understand