Question:
Draw a circle of diameter 6cm. Mark a point Q which is 8cm away from its centre O. Construct tangents QA and QB. Measure their lengths.
Answer:
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.
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