Question

Draw a circle of radius 2-5 cm. Take a point P at a distance of 8 cm from
its centre. Construct a pair of tangents from the point P to the circle.​

Answer 1

To prove pair of tangents point P to the circle is tangent, angle in a semi circle PQO is 90 degree then PQ is tangent simultaneously PR is tangent.

Step-by-step explanation:

Construct 2.5 cm radius of circle O with the help of compass.

Measure 2.5 cm in scale and create a circle from point O.

Use the scale and draw a line 8 cm with help of scale join PO.

Now from P to O, We have to make a tangent.

Create a perpendicular bisector with the help of compass.

To create perpendicular bisector increase compass more than half.

Create to x on top and bottom join the line at M.

We know mid point of M need to take a radius MO draw a circle.

After drawing a circle, We create Tangent line from PQ and PR.

If Angle PQO and Angle PRO are 90 degree then we have proved.

Then It is proved It is a tangent. from the point P to circle.

Answer 2

To prove pair of tangents point P to the circle is tangent, angle in a semi circle PQO is 90 degree then PQ is tangent simultaneously PR is tangent.

Step-by-step explanation:

Construct 2.5 cm radius of circle O with the help of compass.

Measure 2.5 cm in scale and create a circle from point O.

Use the scale and draw a line 8 cm with help of scale join PO.

Now from P to O, We have to make a tangent.

Create a perpendicular bisector with the help of compass.

To create perpendicular bisector increase compass more than half.

Create to x on top and bottom join the line at M.

We know mid point of M need to take a radius MO draw a circle.

After drawing a circle, We create Tangent line from PQ and PR.

If Angle PQO and Angle PRO are 90 degree then we have proved.

Then It is proved It is a tangent. from the point P to circle.