Q2 of 805 Page 11

Construct a tangent to a circle of radius 4 cm from a point on the concentric circle of radius 6 cm and measure its length. Also verify the measurement by actual calculation.

Step 1: Take a point O as a center, draw a circle of 4cm Radius.



Step 2: Again taking O as a center, draw a circle of 6 cm radius. Take a point P on big circle and join OP.


Step 3: Bisect OP. We get midpoint of OP, that is M.


Step 4: Draw a circle of OM radius, in which M is center. Let this intersects small circle at Q and R.


Step 5: Now join PQ and PR.



In ∆PQO,


∠PQO=90° (PQ is a tangent)


PQ=6cm


OQ=4cm


By Pythagoras theorem in


PQ2+OQ2=PO2


PQ2+ 42= 62


PQ2+16 =36


PQ2=20


PQ=2√5


PQ= 4.47 cm


JUSTIFICATION


Join OQ and OR


∠PQO=90° (∵Angle is on semicircle)


OQ⊥PQ


Since OQ is the radius of circle , PQ and PR are tangents


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