Question

example 4.31 draw a circle of diameter 6cm from ,a point p,which in 8cm away from its centre. draw the tangents pa and PB to the circle and measure their lengths ​

Answer 1

Answer:

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Step-by-step explanation:

Given, diameter of the circle = 6 cm

So, the radius of the circle = 6/2 = 3 cm

Let O is the center of the circle

Steps of Construction:

1. Draw a line segment OQ = 8

2. Make perpendicular bisector of OQ which intersects OQ at O1

3. Take O1 Q as radius and draw another circle.

4. Now, from point Q, draw tangents to points of intersections between the two circles.

So, QA and QB are two tangents.

Now, from the figure,

QA2 = 82 - 32

=> QA2 = 64 - 9

=> QA2 = 55

=> QA = √55

Since QA = QB

Hence, QA = QB = √55 cm

So, the lenght of each tangents are √55 cm.