**EXERCISE 16.1**

**1. Use a ruler and compass only in this question.**

**(i) Draw a circle, centre O and radius 4 cm.**

**(ii) Mark a point P such that OP = 7 cm.**

**Construct the two tangents to the circle from P. Measure and record the length of one of the tangents.**

**Solution:**

**2. Draw a line AB = 6 cm. Construct a circle with AB as diameter. Mark a point P at a distance of 5 cm from the mid-point of AB. Construct two tangents from P to the circle with AB as diameter. Measure the length of each tangent?**

**Solution:**

**3. 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:**

**4. Draw a circle of radius 3 cm. Take two points P and Q on one of its extended diameter each at a distance of 7 cm from its centre. Draw tangents to the circle from these two points P and Q.**

**Solution:**

**5. Draw a line segment AB of length 8 cm. Taking A as centre, draw a circle of radius 4 cm and taking B as centre, draw another circle of radius 3 cm. Construct tangents to each circle from the centre of the other circle.**

**Solution:**

**EXERCISE 16.2**

**1. Draw an equilateral triangle of side 4 cm. Draw its circumcircle.**

**Solution:**

**2. Using a ruler and a pair of compasses only, construct:**

**(i) A triangle ABC given AB = 4 cm,BC = 6 cm and ∠ABC = 90°.**

**(ii) A circle which passes through the points A,B and C and mark its centre as O.**

**Solution:**

**3. Construct a triangle with sides 3 cm,4 cm and 5 cm. Draw its circumcircle and measure its radius.**

**Solution:**

**4. Using a ruler and compasses only:**

**(i) Construe a triangle ABC with the following data:**

**Base AB = 6 cm,AC = 5.2 cm and ∠CAB = 60°.**

**(ii) In the same diagram, draw a circle which passes through the points A,B and C. and mark its centre O.**

**Solution:**

**5. Using ruler and compasses only, draw an equilateral triangle of side 5 cm and draw its inscribed circle. Measure the radius of the circle.**

**Solution:**

**6. (i) Conduct a triangle ABC with BC = 6.4 cm,CA = 5.8 cm and ∠ ABC = 60°. Draw its incircle. Measure and record the radius of the incircle.**

**(ii) Construct a ∆ABC with BC = 6.5 cm,AB = 5.5 cm,AC = 5 cm. Construct the incircle of the triangle. Measure and record the radius of the incircle.**

**Solution:**

**7. The bisectors of angles A and B of a scalene triangle ABC meet at O.**

**(i) What is the point O called?**

**(ii) OR and OQ is drawn a perpendicular to AB and CA respectively. What is the relation between OR and OQ?**

**(iii) What is the relation between ∠ACO and ∠BCO?**

**Solution:**

**8. Using ruler and compasses only, construct a triangle ABC in which BC = 4 cm,∠ACB = 45° and the perpendicular from A on BC is 2.5 cm. Draw the circumcircle of triangle ABC and measure its radius.**

**Solution:**

**9. Construct a regular hexagon of side 4 cm. Construct a circle circumscribing the hexagon.**

**Solution:**

**10. Draw a regular hexagon of side 4 cm and construct its incircle.**

**Solution:**