A chord 12 cm long is 8 cm away from the circle What is the length of the chord - Maths - Circles

Question

A chord 12 cm long is 8 cm away from the circle What is the length
of the chord which Is 6 cm away from the centre

Manbar Singh · Accepted Answer

Let AB and CD are 2 chords of the circle that is having the centre at O
Now, AB = 12 cmDraw OL⊥AB and OM⊥CD
Now, OL = 8 cm  and OM = 6 cmWe know that ⊥ drawn from the centre to the chord bisects the chord
Since OL⊥AB, then OL bisects AB, that meansAL = LB = AB2 = 6 cmJoin OA
In ∆OLA,    OA2 = OL2 + AL2   Pythagoras theorem⇒OA2 = 82+62⇒OA2 = 64+36⇒OA2 = 100⇒OA = 10 cmSo, radius of the circle = 10 cmNow, join OC
In ∆OMC,   OC2 = OM2+CM2    Pythagoras theorem⇒102 = 62+CM2⇒CM2 = 100 - 36⇒CM2 = 64⇒CM = 8 cmWe know that ⊥ drawn from the centre to the chord bisects the chord
Since OM⊥CD, then OM bisects CD, that means     CM = MD = CD2⇒CD = 2CM = 2 × 8 = 16 cmHence, CD = 16 cm

A chord 12 cm long is 8 cm away from the circle. What is the length of the chord which Is 6 cm away from the centre.