construct a tangent to a point O of radius 4cm from a point on the concentric circles of radius 6cm and measure it's length .also verify the measurements by actually calculation .write the construction also .
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Explanation:
STEPS OF CONSTRUCTION:
1.Draw two concentric circles C1 and C2 with common Centre O and radius 4 cm 6 cm.
2. Take any point P on outer circle C2 and join OP.
3. Draw the bisector of OP which bisect OP at M’.
4. Taking M’ as centre and OM’ as radius draw a dotted circle with cuts the inner circle C1 at two points M & P’.
5.Join PM & PP’ . Thus PM & PP’ are Required tangents.
On measuring PM & PP’,
PM = PP’ = 4.4 cm
By calculation:
In ∆ OMP, ∠PMO= 90°
PM² = OP² - OM²
[ by Pythagoras theorem]
PM² = (6)² -(4)²
= 36 - 16 = 20
PM² = 20 cm
PM = √20 = 4.4 cm
Hence, the length of the tangents is 4.4 cm.
HOPE THIS WILL HELP YOU.....
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