6. Draw a pair of tangents from a point 10cm away from the centre of circle
of radius 6cm.
7. The difference between the two numbers is 26 and one number is three
times the other. Find the numbers.
8. Find the ratio in which the line segment joining the points (-3 , 10) and
(6,- 8) is divided by (-1, 6).
- Answer the following.
3 x 9 = 27
1. Prove that the lengths of tangents drawn from an external point to a circle
are equal.
2. Construct a pair of tangents to a circle of radius 3cm such that the angle
between the tangents is 400
3. In the given figure AD IN BO prove that AB2 + CD2 - BD2 + A02
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Answer:
ANSWER
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:
OX
2
+PX
2
=OP
2
6
2
+PX
2
=10
2
PX
2
=100−36
PX
2
=64
PX=8 cm
Thus, the length of the tangents is 8 cm.
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