Question

Draw a circle of radius 6 cm and construct tangents to it from an external point from an external point 10 cm away from the center. Measure and verify the lengths of the tangents.

Answer 1

Hint: In order to solve this problem we need to apply the Pythagoras theorem on the triangle we got after drawing the tangent from the information provided to get the length of tangent.

Complete Step-by-Step solution:
The figure for this problem can be drawn as:

The figure has been drawn from the given information that the circle is of radius I 6 cm and tangents are drawn to it from 10 cm from the center.
We know that tangents at radius are at right angles.
So, we can apply the Pythagoras theorem on triangle ABO right angle at A.
So we do,
${\text{B}}{{\text{O}}^{\text{2}}}{\text{ = A}}{{\text{O}}^{\text{2}}}{\text{ + A}}{{\text{B}}^{\text{2}}}$
We can see from the diagram that AO = 6cm, BO = 10cm
On putting the value of AO and BO we get,
 $
  {10^{\text{2}}}{\text{ = }}{{\text{6}}^{\text{2}}}{\text{ + A}}{{\text{B}}^{\text{2}}} \\
  A{B^2} = 100 - 36 = 64 \\
  AB = 8 \\
$
Since the square root of 64 is 8.
Hence the length of tangents AB = BC = 8 cm.

Note: In these types of problems of circles you need to use the properties of tangent. Here we have used the properties tangent that angle between radius and tangent is 90 degrees, tangents from a single point on the circle are of equal length and we have applied Pythagoras in triangle AOB to get the solution to this problem.