The length of a tangent from a point A at distance 5cm from the centre of
the circle is 4cm. Find the diameter of the circle
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⇒ Given:
The length of a tangent from a point A at distance 5 cm from the center of the circle is 4 cm.
[Please refer the attachment to view the figure.]
⇒ To Find:
The diameter of the circle.
⇒ Solution:
In the figure:
AX is the tangent and AO is the distance between the point A and the center of the circle. OX is a radius.
As AX is a tangent,
OX ⊥ XA meaning that ΔAOX is a right angled triangle.
Using the Pythagoras theorem:
Altitude² + Base² = Hypotenuse²
4² + OX² = 5²
OX² = 5² - 4²
OX² = 25 - 16
OX² = 9
OX = 3 cm
OX is the radius of the circle. This means that doubling it [creating a diameter], its measure would be:
3 x 2 = 6 cm
The length of the diameter is 6 cm.
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