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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

By Athena

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​

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Athena

the product of 8 and a number is 72.
what is the number?​

A labour is engaged for 50 days on the condition that he will get rs 25 each day and will give rs 10 if he is absent. if he works

2 thoughts on “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”

  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.

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