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

Answer:

**Solution:**

Steps to construct:

Step 1: Mark a point O.

Step 2: With center O and radius 4cm and 6cm, draw two concentric circles.

Step 3: Join OA and mark its mid-point as M.

Step 4: With center M and radius MA, draw another circle which intersects the first circle at P and Q.

Step 5: Join AP and AQ. Hence, AP and AQ are the required tangents to the first circle from point A and are of measurement 4.5 cm each.

For verification:

Join OP, than in triangle OPA,

OA^{2}= OP^{2}+PA^{2}

6^{2} = 4^{2} + PA^{2}

PA^{2}= 36-16=20

PA= 4.5 cm

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