the length of tangent to a circle which is 13cm distance from the centre of the circle is 12cm find the radius of the circle
Answers
Radius of circle = 5 cm if the length of tangent to a circle which is 13cm distance from the centre of the circle is 12cm
Step-by-step explanation:
Let say Cenetr of circle = O
Tangent PA is drawn from point P touching circle at A
OP = 13 cm ( Distance of point from center of Circle)
PA = 12 cm ( Length of Tangent)
OA = Radius = ?
Applying Pythagorean theorem
OP² = PA² + OA²
=> 13² = 12² + Radius²
=> 169 = 144 + Radius²
=> Radius² = 25
=> Radius² = 5²
=> Radius = 5 cm
Radius of circle = 5 cm
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Answer:
13^2 = 12^2 + r^2
169–144 = r^2
r^2 = 25
r = 5
Step-by-step explanation:
radius is perpendicular to the tangent line at the tangent point, the three lines form a right triangle. The hypotenuse is 13, one side is 12 and the radius is the third side. By the Pythagorian theorem, the radius is 5.