Advertisements
Advertisements
Question
Using ruler and compasses only construct a triangle ABC in which BC = 4 cm, ∠ACB = 45° and perpendicular from A on BC is 2.5 cm. Draw a circle circumscribing the triangle ABC and measure its radius.
Solution
Steps of construction:
- Draw a line segment BC = 4 cm.
- At C, draw a perpendicular line CX and from it, cut off CE = 2.5 cm.
- From E, draw another perpendicular line EY.
- From C, draw a ray making an angle of 45° with CB, which intersects EY at A.
- Join AB.
- ΔABC is the required triangle.
- Draw perpendicular bisectors of sides AB and BC intersecting each other at O.
- With centre O, and radius OB, draw a circle which will pass through A, B and C.
Measuring the radius OB = OC = OA = 2 cm.
APPEARS IN
RELATED QUESTIONS
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 5 cm. Draw two tangents to this circle so that the angle between the tangents is 45°.
Construct a circle, inscribing an equilateral triangle with side 5.6 cm.
Draw a circle with the help of a bangle. Take any point P outside the circle. Construct the pair of tangents form the point P to the circle
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.
In Figure 2, PQ is a chord of length 8 cm of a circle of radius 5 cm. The tangents at P and Q intersect at a point T. Find the length TP.
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.
Draw a circle of radius 3 cm and construct a tangent to it from an external point without using the center.
To draw a pair of tangents to a circle which are inclined to each other at an angle of 35°. It is required to draw tangents at the end points of those two radii of the circle, the angle between which is ______.
Construct a pair of tangents to a circle of radius 3 cm which are inclined to each other at an angle of 60°.
