# ML Aggarwal Solutions Class 10 Mathematics Solutions for Constructions Exercise 16.1 in Chapter 16 - Constructions

Question 4 Constructions Exercise 16.1

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.

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,

OA2= OP2+PA2

62 = 42 + PA2

PA2= 36-16=20

PA= 4.5 cm

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