SOLUTION: In the diagram to the left, circle with centre O has a radius of 7 cm. Segment AT is tangent to the circle. AO = 25 cm, and AX = XY (this length is labeled m). Find the length of m

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Question 1208908: In the diagram to the left, circle with centre O has a radius of 7 cm. Segment AT is tangent to the circle. AO = 25 cm, and AX = XY (this length is labeled m). Find the length of m.
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Found 2 solutions by ikleyn, mccravyedwin:
Answer by ikleyn(52850)   (Show Source): You can put this solution on YOUR website!
.

From the diagram, find AO = 18+7 = 25 cm.
Find the length of AT from the right triangle AOT

    AT =  =  = 24.


Next, consider right triangle XOT.


In this triangle, the leg XT is  AT-m = 24-m cm;

                  the leg OT is 7 cm;

                  the hypotenuse OX is 7+m cm.


Write the Pythagorean equation

     +  = .


Simplify

    576 - 2*24m + m^2 + 49 = 49 + 2*7*m + m^2,

    576 - 48m = 14m 

    576 = 48m + 14m

    576 = 62m

    m = 576/62 = 288/31 = 9.290 cm  (rounded).


ANSWER.  m =  = 9.290 cm.

Solved.



Answer by mccravyedwin(408)   (Show Source): You can put this solution on YOUR website!

 

Let z = XT

By the Pythagorean theorem on right triangle ATO








By the Pythagorean theorem on right triangle XTO










Exact value of  or about 9.29 cm

Edwin
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