Advertisements
Advertisements
Question
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.
Advertisements
Solution
Steps of construction:
- Draw a line segment AB = 4 cm.
- With A as the centre and radius = 6 cm, draw an arc.
- With B as centre and radius = 6 cm, draw another arc intersecting the previous arc at point C.
- Join A to C and B to C. Then, △ABC is the required isosceles triangle (AC = 6 cm, BC = 6 cm, AB = 4 cm).
- Draw the bisector of angle ∠CAB.
- Draw the bisector of angle ∠CBA. These angle bisectors intersect at point O. Then O is the incentre of △ABC.
- Draw OP ⟂ AB. (From O, drop a perpendicular to the base AB.
Let the foot of the perpendicular be P.) - With O as centre and radius = OP, draw a circle touching all three sides of the triangle. This is the required incircle of △ABC.
- By measurement, OP gives the radius of the incircle.
RELATED QUESTIONS
Draw a circle with the help of a bangle. Take a point outside the circle. Construct the pair of tangents from this point to the circles. Give the justification of the construction.
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.
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 of radius 4.2. Draw a pair of tangents to this circle inclined to each other at an angle of 45°
Draw a pair of tangents to a circle of radius 3 cm, which are inclined to each other at an angle of 60°.
Using ruler and compasses only, draw tangents to a circle of radius 3 cm from a point 5 cm from the centre. What is the length of each of them ?
Take a point O on the plane at the paper. With O as center draw a circle of radius 3 cm. Take a point P on this circle and draw a tangent at P.
Draw two lines AB, AC so that ∠ BAC = 40°:
(i) Construct the locus of the center of a circle that touches AB and has a radius of 3.5 cm.
(ii) Construct a circle of radius 35 cm, that touches both AB and AC, and whose center lies within the ∠ BAC.
To draw a pair of tangents to a circle which are inclined to each other at an angle of 60°, it is required to draw tangents at end points of those two radii of the circle, the angle between them should be ______.
Construct a pair of tangents to a circle of radius 3 cm which are inclined to each other at an angle of 60°.
