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प्रश्न
- Using ruler and compasses only, construct a triangle ABC in which AB = 8 cm, BC = 6 cm and CA = 5 cm.
- Find its in centre and mark it I.
- With I as centre, draw a circle which will cut off 2 cm chords from each side of the triangle. What is the length of the radius of this circle.
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उत्तर
Steps of construction:
- Draw a line segment BC = 6 cm.
- With centre B and radius 8 cm draw an arc.
- With centre C and radius 5 cm draw another arc which intersects the first arc at A.
- Join AB and AC.
ΔABC is the required triangle. - Draw the angle bisectors of ∠B and ∠A intersecting each other at I. Then I is the incentre of the triangle ABC.
- Through I, draw ID ⊥ AB.
- Now from D, cut off `DP = DQ = 2/2 = 1 cm`.
- With centre I and radius IP or IQ, draw a circle which will intersect each side of triangle ABC cutting chords of 2 cm each.
संबंधित प्रश्न
Draw a circle of radius 3 cm. Draw a pair of tangents to this circle, which are inclined to each other at an angle of 60º.
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.
In the given figure, PQ is a tangent to the circle at A. AB and AD are bisectors of ∠CAQ and ∠PAC. if ∠BAQ = 30°. Prove that:
- BD is a diameter of the circle.
- ABC is an isosceles triangle.
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 pair of tangents to a circle of radius 4.5 cm, which are inclined to each other at an angle of 45°.
Draw two circles of radii 3 cm and 3.5 cm, their centres being 8 cm apart. Construct a transverse common tangent and measure its length.
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 ______.
Which of the following is not true for a point P on the circle?
Construct a pair of tangents to a circle of radius 3 cm which are inclined to each other at an angle of 60°.
Draw a circle of radius 2.5 cm. Construct a pair of tangents from a point Pat a distance of 6 cm from the centre of the circle.
