Advertisements
Advertisements
प्रश्न
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
उत्तर
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.
APPEARS IN
संबंधित प्रश्न
Draw a circle of radius 6 cm. From a point 10 cm away from its centre, construct the pair of tangents to the circle and measure their lengths. Give the justification of the construction.
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.
Draw an inscribing circle of a regular hexagon of side 5.8 cm.
Construct a triangle ABC in which base BC = 5.5 cm, AB = 6 cm and ∠ABC = 120°.
- Construct a circle circumscribing the triangle ABC.
- Draw a cyclic quadrilateral ABCD so that D is equidistant from B and C.
Draw a circle of radius 3 cm. Form 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.
Construct a tangent to a circle of radius 4 cm from a point on the concentric circle of radius 6 cm and measure its length. Also, verify the measurement by actual calculation.
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.
Draw a pair of tangents to a circle of radius 4.5 cm, which are inclined to each other at an angle of 45°.
Which of the following is not true for a point P on the circle?
A pair of tangents can be constructed from a point P to a circle of radius 3.5 cm situated at a distance of 3 cm from the centre.
