Question

Study the following figure, where two concentric circles share center C.

Segment AB is a diameter of the larger circle.
Segment AB intersects a chord of the smaller circle, PQ, at a right angle at point Z.
Segment AB intersects a chord of the larger circle, MN, at a right angle at point 0.

If MO=7x-4, and NO=6x, what is the length of MN

Answer 1

Length of MN = 48 units

Explanation:

AB is the diameter of the larger circle which is perpendicular to both the chords PQ (chord of the smaller circle) and MN(chord of the larger circle).

Theorem says,

"Radius or a diameter of a circle which is perpendicular to the chord divides the chord in two equal parts."

Therefore, MO ≅ ON

m(MO) = m(ON)

7x - 4 = 6x

7x - 6x = 4

x = 4

m(MN) = m(MO) + m(ON)

= (7x - 4) + (6x)

= 13x - 4

= (13 × 4) - 4

= 52 - 4

= 48

Length of chord MN will be 48 units.