SOLUTION: In the diagram below, circle with centre O has a radius of 5 cm. Segment AT is tangent to the circle. AO = 13 cm, and AX = XY (this length is labeled m). Find the length of m.
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Question 1204853: In the diagram below, circle with centre O has a radius of 5 cm. Segment AT is tangent to the circle. AO = 13 cm, and AX = XY (this length is labeled m). Find the length of m.
https://ibb.co/6HKJNjR Found 2 solutions by mananth, ikleyn:Answer by mananth(16949) (Show Source):
You can put this solution on YOUR website!
From Figure
13^2= AT^2+5^2 ( Pythagoras theorem) OAT
AT^2 = 144 ,AT =12
'
OX =m+5, XT =(12-m)
(m+5)^2= 5^2+(12-m)^2 ( Pythagoras theorem) OMT
Find m
You can put this solution on YOUR website! .
In the diagram below, circle with center O has a radius of 5 cm. Segment AT is tangent to the circle.
AO = 13 cm, and AX = XY (this length is labeled m). Find the length of m.
https://ibb.co/6HKJNjR
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This problem is not difficult.
First of all, from triangle AOT, AT = = = = 12 cm.
Next, consider triangle XTO.
Its leg XT has the length (12-m) cm. It is the tangent segment to the circle O.
Continue XO further to intersection with the circle O.
You will get the long secant of the length m+5+5 = m + 10 cm.
The outer part of this secant has the length m.
Using well known property of the tangent segment, secant and its outer part, you can write this equation
= m*(m+10),
which is
= m*(m+10).
Simplify and find "m"
144 - 24m + m^2 = m^2 + 10m
144 = 10m + 24m
144 = 34m
m = = cm = 4 cm. ANSWER
