Question

In the figure, A and B are the centres of
two circles touching each other externally
at M. Line AC and line BD are the
tangents. If AD = 6 cm, BC = 9 cm, then
find the lengths of seg AC and seg BD.​

Answer 1

Answer:

for answer please see picture

Answer 2

The lengths of seg AC and seg BD are 12 cm and 13.7 cm

Step-by-step explanation:

here ,

AD = 6 cm

BC = 9 cm

AD = AM and BC = BM (radii of the circles )

then AB = AM + BM

= 6+9 = 15 cm

since , we know that the A tangent to a circle forms a right angle with the circle's radius, at the point of contact of the tangent.

then using the pythagoras theorem

in triangle ADB

AB² = AD²+BD²

15²= 6²+BD²

BD² =225 - 36

BD² = 189

BD = √189 = 13.7  cm

then similarly in triangle ACB

AB² = BC²+ AC²

15²= 9²+ AC

AC ² = 225- 81

AC²= 144

AC = √144 = 12 cm

hence ,

The lengths of seg AC and seg BD.  are 12 cm and 13.7 cm

#Learn more:

In the adjoining figure, O is the centre and seg AB is a diameter. At the point C on the circle, the tangent CD is drawn. Line BD is a tangent to the circle at the point B. Show that seg OD ||chord AC​

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