Question

radius of the circle is 0 is 41 unit length of a chord PQ is 80 unit find the distance of the chord from the centre of the circle​

Answer 1

Answer:

9 unit

Step-by-step explanation:

Hope it will help you

Answer 2

Step-by-step explanation:

Given: In a circle with centre O,  OP is radius and PQ is its chord,  seg OM ⊥ chord PQ, P-M-Q  OP = 41 units, PQ = 80 units, 

To Find: Distance of the chord from the centre of the circle(OM)

i. (1/2) PM = (PQ) [Perpendicular drawn from the centre of a circle to the chord bisects the chord.]

= (1/2) (80) = 40 Units ….(i) 

ii. In ∆OMP, ∠OMP = 90° 

∴ OP2 = OM2 + PM2 [Pythagoras theorem]

  ∴ 412 = OM2 + 402 [From (i)] 

∴ OM2 = 412 – 402  = (41 - 40) (41 + 40) [a2 – b2 = (a – b) (a + b)]  = (1)(81)

∴ OM2 = 81 

OM = √81 = 9 units [Taking square root on both sides] [From (i)] 

∴ The distance of the chord from the centre of the circle is 9 units.