Advertisements
Advertisements
Question
Draw a circle at a radius of 4 cm. Take a point on it. Without using the centre at the circle, draw a tangent to the circle at point P.
Advertisements
Solution
Steps of Construction:
(i) Draw a chord PQ through the given point on the circle.
(ii) Take a point R on the circle and join P and Q to a point R.
(iii) Construct ∠ QPY = ∠ PRQ on the opposite sides of the chord PQ.
(iv) Produce YP to X' to get YPX as the required tangent.
Construct a tangent to the circle from an external point:
In this section we shall study the construction at tangent to a circle from an external point when its center is; (i) Know (ii) Unknown
Type (I). Construction at tangent to a circle from an external point when its centre is known.
Steps of Construction:
(i) Join the centre O of the circle to the given external point P i.e., join OP.
(ii) Draw right bisector of OP, intersecting OP at Q.
(iii) Taking Q as centre and OQ = PQ as radius, draw a circle to intersect the given circle at T and T'.
(iv) Join PT and PT' to get the required tangents as PT and PT'.
APPEARS IN
RELATED QUESTIONS
Draw a circle of radius 4 cm. Draw two tangents to the circle inclined at an angle of 60° to each other.
In the figure given below, O is the centre of the circle and SP is a tangent. If ∠SRT = 65°,
find the value of x, y and z.
In the figure given below, diameter AB and chord CD of a circle meet at P. PT is a tangent to the circle at T. CD = 7.8 cm, PD = 5 cm, PB = 4 cm. Find:
1) AB.
2) the length of tangent PT.
Draw a circle of radius 3 cm. Mark a point P at a distance of 5 cm from the centre of the circle drawn. Draw two tangents PA and PB to the given circle and measure the length of each tangent.
Draw a circle with centre O and radius 3 cm. Take a point P outside the circle. Draw tangents to the circle from P without using the centre and using only ruler and compasses.
Draw two circles of radii 2.5 cm and 3.5 cm respectively so that their centres are 8 cm apart. Draw direct comm on tangents to the circle.
Draw two circles of radii 3.5 cm and 2 cm respectively so that their centres are 6 cm apart. Draw direct common tangents to the circle and show that they are equal in length.
Draw an isosceles triangle with sides 6 cm, 4 cm, and 6 cm. Construct the incircle of the triangle. Also, write the steps of construction.
A pair of tangents can be constructed from a point P to a circle of radius 3.5cm situated at a distance of ______ from the centre.
Construct a pair of tangents to a circle of radius 3 cm which are inclined to each other at an angle of 60°.
