Drawing Tangents to a Circle from a Point outside the Circle

Q. Question 3
Draw two concentric circles of radii 3 cm and 5 cm. Taking a point on outer circle construct the pair of tangents to the other. Measure the length of a tangent and verify it by actual calculation.

Q.

Write the steps of construction to construct the tangents to a circle from an external point.

Q.

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.

Q. Draw a circle of radius 3.3 cm Draw a chord PQ of length 6.6 cm. Draw tangents to the circle at points P and Q. Write your obeservation about the tangents.

Q.

PQR is a right angled triangle with PQ = 3 cm, QR = 4cm. A circle which touches all the sides of the triangle is inscribed in the triangle. Calculate the radius of the circle.

1. r = 2cm

2. r = 4cm

3. r = 5cm

4. r = 1cm

Q. Construct a tangent to a circle with centre P and radius 3.2 cm at any point M on it.

Q.

Draw a pair of tangents to a circle of radius $5\mathrm{cm}$ which is inclined to each other at an angle of $60°$. Give the justification of the construction.

Q.

Draw two tangents to a circle of radus 3.5 cm from a point P at a distance of 6.2 cm from its centre.

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

Q.

Draw a circle of radius 3 cm. Take two points P and Q on one of its diameters extended on both sides, each at a distance of 7 cm on opposite sides of its centre. Draw tangents to the circle from these two points P and Q.

Q.

Draw a circle of radius 4.5 cm. Draw two tangents to this circle so that the angle between the tangents is ${60}^{\circ }.$

Q.

Draw a circle of radius 3 cm. Draw a tangent to the circle making an angle of ${30}^{\circ }$ with a line passing through the centre.

Q.

Draw a circle of radius $6cm$ . From a point $10cm$ away from its centre, construct the pair of tangents to the circle and measure their lengths. Give the justification of the construction

Q.

Draw a circle with the help of a bangle. Take any point P outside the circle. Construct the pair of tangents from the point P to the circle.

Q.

Draw a circle of radius 3 cm. From a point P, 7 cm away from the centre of the circle, draw two tangents to the circle. Also, measure the lengths of the tangents.

Q.

Draw a circle of radius 4.2 cm. Draw a pair of tangents to this circle inclined to each other at an angle of ${45}^{\circ }$.

Q.

Draw a circle of radius 3.5 cm. Mark a point P outside the circle at a distance of 6 cm from the centre. Construct two tangents from P to the given circle. Measure and write down the length of one tangent.

Q. Draw a circle with radius 4.1 cm. Construct tangents to the circle from a point at a distance 7.3 cm from the centre.

Q.

Draw a circle of diameter 9 cm. Mark a point at a distance of 7.5 cm from the centre of the circle. Draw tangents to the given cirlce from this exterior point. Measure the length of each tangent.

Q.

Draw a circle of radius 6 cm.Construct the two tangents to the circle from a P which is at the distance of 9 cm from centre. Measure the length of the tangents.

1. 4.7 cm

2. 6.7 cm

3. 7.7 cm

4. 5.7 cm

Q. Question 6
Let ABC be a right triangle in which AB = 6 cm, BC = 8 cm and $\angle B={90}^{\circ }$. BD is the perpendicular from B on AC. A circle through B, C, D is drawn. Construct the tangents from A to this circle.

Q.

Draw a circle of radius 6 cm. From a point 10 cm away from its centre, construct a pair of tangents to the circle and find their lengths.

1. 2 cm, 5 cm

2. 8 cm, 8 cm

3. 3 cm, 8 cm

4. 5 cm, 7 cm

Q.

Which of the following parameters given in the figure are enough to construct the figure (choose the minimum number of parameters possible):

Distance AO = d

Radius of the bigger circle (with center A) = R

Radius of the smaller circle (with center B) = r

$\angle$POA = $\theta$

Note that other than the parameters given in an option, nothing else is given and you have to come up with the figure as given above.

1. R, d,

2. R, r, d, AO, BO

3. AO, BO, d

4. R, d, r

Q. Draw a circle with radius 3.4 cm. Draw a chord MN of length 5.7 cm in it. construct tangents at point M and N to the circle.

Q. Draw a triangle ABC with side AB =6cm, BC=8cm and angle B is 90°. BD is the perpendicular from B to AC. The circle through B, C, D is drawn. Construct the tangents from A to this circle.

Q.

Prove that the parallelogram circumscribing a circle, is a rhombus.

Q. Construct a circle of radius 7cm. From a point 10 cm away from its centre, draw tangents to the circle.

Q.

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

Q. Draw a circle of radius 3.5 cm. Mark s point P outside the circle at a distance of 6 cm from the centre, construct two tangents from P to the given circle. Measure and write down the length of one tangent.

Q. Sketch tangent to a given circle with radius 4 cm.