AB is a tangent to a circle with centre P and B is the point of contact. PA intersects the circle at C. If AB=15cm and AC = 9cm.Find the radius of the circle
Answers
Step-by-step explanation:
So this is how the figure will look i hope much is clear from figure. This a abit rough sketch .
over here we already know why this is a right angle triangle as radius is perpendicular to the tangent at the point of contact .
Now,
(ab)^2 +( bp)^2 = (ap)^2
Note:- if u ever hv confusion in understanding the hypotenuse then remember that it will be the side opposite to 90°.
Now putting values,
(15)^2 + r^2 = ( 9 + r)^2
225 + r^2 = 81 + r^2 + 18r
r^2 gets cancelled ,
225-81 = 18r
144 /18 = r
8 = r
So the value of radius is 8 cm . Hope it was helpful.
You can even cross check by putting value of 8 in the pythogoras theorem,
both sides will come out to be 17 .
Given : AB is a tangent to a circle with centre P and B is the point of contact.
PA Intersects the circle at C.
AB = 15 cm and AC = 9 cm,
To find : the radius of the circle
Solution:
AP² = AB² + PB²
PB = r cm = Radius of circle
AP = AC + CP
CP = Radius of circle
=> AP = 9 + r cm
AB = 15 cm
=> (9 + r)² = 15² + r²
=> 81 + r² + 18r = 225 + r²
=>18r = 144
=> r = 8 cm
Radius of circle = 8 cm
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