Construct a triangle XYZ in which XY = YZ = 4.5 cm and ZX = 5.4 cm. Draw the circumcircle of the triangle.

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Solution

Steps of Construction:

(i) Draw a line segment XY = 4.5 cm
(ii) With the help of a compass, draw an arc of 4.5 cm from Y as centre.
(iii) Again with the help of compass, draw another arc of 5.4 cm from X as centre which intersects the previous arc made by Y.
(iv) Now, mark the intersection as point Z and join it to both X and Y. The required triangle XYZ is obtained.
(v) Draw the bisectors of XY and YZ which meet at point O.
(vi) Now, draw the circle using a compass taking O as centre and radius OX or OY or OZ.
(vii) This circle will pass through the vertices X, Y and Z.

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Similar questions

△ X Y Z

X Y = 4.5

Y Z = 5

Z X = 6

△ X Y Z

X Y = 4.5 c m, Y Z = 5 c m

Z X = 6 c m

Construct a triangle XYZ in which ∠Y = 30°, ∠Z = 90° and XY + YZ + ZX = 11 cm.

∠ Y

30^{0}

∠ Z

90^{0}

∠ Y = 30^{\circ}, ∠ Z = 90^{\circ} a n d X Y + Y Z + Z X = 11 c m

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