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 line segment AB of length 7 cm. Taking A as centre, draw a circle of radius 3 cm and taking B as centre, draw another circle of radius 2 cm. Construct tangents to each circle from the centre of the other circle.
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 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.
Construct an equilateral triangle ABC with side 6 cm. Draw a circle circumscribing the triangle ABC.
Construct a circle, inscribing an equilateral triangle with side 5.6 cm.
A park is of the shape of a circle of diameter 7 m. It is surrounded by a path of width of 0·7 m. Find the expenditure of cementing the path, if its cost is Rs 110 per sq. m ?
Draw a pair of tangents to a circle of radius 4.5 cm, which are inclined to each other at an angle of 45°.
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.
A pair of tangents can be constructed to a circle inclined at an angle of 170°.
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.
