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Question

Draw the two tangents from a point which is 10cm away from the centre of a circle of radius 6cm. Also, measure the lengths of the tangents.

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Solution

Step 1: With O as the center draw a circle of radius 6 cm.

Step 2: Mark a point P at a distance of 10 cm from O and join OP.

Step 3: Draw the perpendicular bisector of OP. Let it meet OP at M.

Step 4: With M as center and MO as radius, draw another circle.

Step 5: Let the two circles intersect at X and Y.

Step 6: Join PX and PY. They are required tangents.

Thus, this is the resulting figure.

To determine the length of the tangent, consider the triangle OXP and apply Pythagoras theorem to it:

OX2+PX2=OP2

62+PX2=102

PX2=10036

PX2=64

PX=8 cm

Thus, the length of the tangents is 8 cm.

1373360_622496_ans_c97d1ac7c519418d98b2d76095dd73b4.jpg

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