**GEOMETRIC CONSTRUCTION: TANGENTS OF A CIRCLE**

**Tangent and Normal to a Circle**

A tangent is a straight line that touches the circumference of a circle. It is usually at right angles to the radius of the circle.

A normal is a straight line which joins the center of a circle to the tangent at the point of tangency.

**Evaluation**** **

Draw a circle indicating its tangent and normal to the tangent

**Construction of Tangent and Normal to a circle**

**Tangent to a circle from a point on the circumference**

**Steps**

- Draw the circle with center O
- Mark the given point A on the circumference
- Join OA and extends it outwards
- With A as center and radius OA, draw an arc to cut the extended line at B
- The perpendicular bisector of OB is the required tangent
- CD is the tangent to the circle at point A while OB is the normal

**Tangent to a circle from a given point outside the circle**

**Steps**

- Draw the given circle with center O
- Locate point A outside the circle
- Draw line OA
- Construct a semicircle on OA to intersect the given circle at B
- Line AB is the required tangent to the circle

**Tangent to a circle from a given point outside the circle**

**Tangent to two Equal Circles**

**Steps**

- Draw the two circles with centers A and B respectively
- Draw line AB to join the two centers
- Draw a line perpendicular to AB at A to intersect the first circle at D
- Draw a line perpendicular to AB at B to intersect the second circle at C
- CD is the required tangent

**EVALUATION**

- Construct a tangent to a circle of radius 4cm at any point on the circumference.

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