Question

If O is the center of the circle and PQ and PR ne two chords of equal length of each 12 cm .PO intersects QR at S . The find the length of OS

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Answer 1

see figure. A possible rough diagram is drawn. where r is radius of circle, h = PS , RS = a and assuming SO = x.

given, PQ = PR = 12cm.

from ∆PRS,

PS² + RS² = PR² [ Pythagoras theorem]

or, h² + a² = 12² ......(1)

from ∆ROS,

RS² + SO² = RO² [ Pythagoras theorem]

or, a² + x² = r² .......(2)

from equation (1) and (2),

h² - x² = 12² - r²

but from figure it is clear that, h + x = r

so, (r - x)² - x² = 144 - r²

or, r² + x² - 2rx - x² = 144 - r²

or, -2rx = 144 - 2r²

or, x = (72 - r²)/r

hence, value of OS will be (72 - r²)/r , here you see data is insufficient. you can get answer if r is given.