chord AB and CD of a circle intersect each other in point M. the centre of the circle is P. The radius of the circle is 13 cm and PM= 5 cm find the product of CMxDM.
plz help....
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There are two cases
CASE 1:
Assuming point M is the midpoint of chord CD, and M is a point of tangency to the circle M is on with radius 5, it follows that CD ⊥ PM, and two congruent right-triangles are formed. Using Pythagoras, CM = MD = 12 units, and the product of those two lengths will be 144.
CASE 2:
What if M is NOT the midpoint of chord CD, how does this change the result?
My hunch is that it will still be 144, but I am working on a proof which I will submit ASAP.
Hope this helps! Cheers! :)
CASE 1:
Assuming point M is the midpoint of chord CD, and M is a point of tangency to the circle M is on with radius 5, it follows that CD ⊥ PM, and two congruent right-triangles are formed. Using Pythagoras, CM = MD = 12 units, and the product of those two lengths will be 144.
CASE 2:
What if M is NOT the midpoint of chord CD, how does this change the result?
My hunch is that it will still be 144, but I am working on a proof which I will submit ASAP.
Hope this helps! Cheers! :)
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