Math, asked by akhila1441, 1 year ago

A circle of radius 5 cm which has chords AB , CD and AB = 6cm CD= 8cm. If OM perpendicular to CD and ON perpendicular to AB . Find the length of MN

Answers

Answered by muskansingh52
0
sol. by using Pythagoras,om=4cm & on=3cm
then,
mn=om-on
4-3=1cm
Answered by Anonymous
0
Given chords AB=6 cm, CD =12 cm and AB||CD Draw OP⊥ AB. Let it intersect CD at Q and AB at P ∴ AP = PB = 3 cm and CQ = DQ = 6 cm [Since perpendicular draw from the centre of the chord bisects the chord] Let OD = OB = r In right ΔOQD, r2 = x2 + 62 [By Pythagoras theorem] r2 = x2 + 36 → (1) In right ΔOPB, r2 = (x + 3)2 + 32 [By Pythagoras theorem] Þ r2 = x2 + 6x + 9 + 9 = x2 + 6x + 18→ (2) From (1) and (2) we get x2 + 36 = x2 + 6x + 18 ⇒ 6x = 18 ∴ x = 3 Put x = 3 in (1), we get r2 = 32 + 36 = 9 + 36 = 45 ∴ r = √45 = 3√5 cm

hope this helps you out!
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