Draw a pair of tangents to a circle of radius 4 cm from a point outside the circle such that the tangents are inclined at an angle of 70.

Solution:

We can draw the tangents using a property of circles. It is given that the tangents are inclined at an angle of 70. Therefore, the radii joining the points of contacts to the centre of the circle are inclined at an angle of 110 as shown in the figure.

Why is it 110 degree?

As we know that tangent drawn from the external point to a circle is always perpendicular to the radius at the point of contact.
Suppose the 2 tangents are drawn from external point P, that touches the circle at A and B. Let O be the centre of the circle.
Now we will see a quadrilateral PAOB is formed.
If the two tangents are inclined at 70⁰ , then $\angle$APB = 70^0.
also ​$\angle$PAO = ​$\angle$PBO = 90⁰ [As tangent is perpendicular to radius]
so, ​$\angle$AOB = 360⁰ - [70⁰ + 90⁰ + 90⁰] = 360⁰ - 250⁰ = 110⁰