Question

A point P is at distance 13 cm from the centre C of the circle,and PT is a tangent to the given circle. If PT=12 cm,find the radius of the circle

Answer 1

Let O be the centre of Circle,

We know that always, Tangent is perpendicular to the radius, So , If we join the PTO , We will get a Right angled traingle,

The Hypotenuse = Distance OP = 13 cm,
Altitude = Length of tangent PT = 12 cm,

Base = Radius = OT = ?

According to the Pythagoras Theorem,

Hypotenuse ² = Altitude ² + Base ²,
Here base = Radius,

=> 13² = 12² + Radius²
=> Radius² = 169 - 144
=> Radius ² = 25,
=> Radius = 5 cm,

Therefore the radius of Circle is 5 cm,

Hope you understand, Have a great day !!

Answer 2

HEY BUDDY HERE IS UR ANSWER !!

AQ,

HYPOTENUS = 13 = PO
RADIUS = X = OT
OPPOSITE = 12 = PT

NOW ,


BY USING PYTHAHORAS THEOREM ,


(13)^2 = (12)^2 + ( Radius )^2

(Radius)^2 = 169 - 144
(x)^2 = 25
X = 5cm

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