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Question

# Draw ∆ ABC such that l (BC) = 5.5 cm, m∠ABC = 90$°$, l (AB) = 4 cm. Show the orthocentre of the triangle.

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Solution

## Given: In $∆$ABC, BC = 5.5 cm, AB = 4 cm and ∠ABC = 90$°$. To construct: Orthocentre of $∆$ABC. Steps of construction: (i) Draw a line segment BC = 5.5 cm. (ii) At point B, make an $\angle$XBC = 90$°$. (iii) With B as centre and radius = 4 cm, draw an arc intersecting the ray BX at point A. (iv) Join AC. (v) Now, with B as centre and any convenient radius, draw arcs intersecting AC at points D and E. (vi) With D and E as centres and radius more than half of DE, draw arcs intersecting each other point F. (vii) Join BF intersecting AC at point G. Thus, AB, BC and BG are altitudes of $∆$ABC and point of their concurrence is the required orthocentre.

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