Find the value of x in the circle below. round to the nearest tenth, if necessary
Answers
Step-by-step explanation:
Given :-
Length of the tangent = 24 units
Radius = x units
Distance between the centre of the circle and the exterior point = 18 units
To find :-
Find the value of x ?
Solution :-
Given that :
Length of the tangent ( l) = 24 units
Radius of the circle (r) = x units
Distance between the centre of the circle and the exterior point (d)= 18 units
We know that
If the radius is r units , length of the tangent is l units and the distance between the centre of the circle and the exterior point of the circle is
l= √(d²+r²)
=> l² = d²+r²
=>r² = l²-d²
On Substituting these values in the above formula
=> x² = 24² - 18²
=> x² = (24×24) - (18×18)
=> x² = 576 - 324
=>x² = 252
=> x = √252
=> x = √(2×2×3×3×7)
=> x = (2×3)√7
=> x = 6√7
We know that
√7 = 2.645 ...
=> x = 6×2.645...
=>x = 15.87...
=> x = 15.9 units (correct it to one decimal)
Radius of the circle = 15.9 units
Answer:-
The value of x for the given problem is 15.9 units
Used formulae:-
If the radius is r units , length of the tangent is l units and the distance between the centre of the circle and the exterior point of the circle is
l= √(d²+r²)
Answer:
15.9 ________________