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Question
Draw an obtuse angled △LMN. Draw its altitudes and denote the orthocentre by O.
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Solution
Steps of construction :
(i) Draw an obtuse angled △LMN.
(ii) With L as centre and taking convenient radius, draw two arcs that intersect MN at P and Q.
(iii) With P as centre and taking radius more than half of PQ, draw an arc. With Q as centre and taking same radius, draw another arc that intersect the previous arc at R.
(iv) Join LR than intersect MN at I. LI is an altitude the side MN.
(v) Extend NL to a point V.
(vi) With M as centre and taking convenient radius, draw two arcs that intersect NL produced at D and E.
(vii) With D as centre and taking radius more than half of DE, draw an arc. With E as centre and taking same radius, draw another arc that intersect the previous arc at F.
(viii) Join MF that intersect NL produced at K. MK is an altitude to side NL produced.
(ix) Extend ML to point U.
(x) With N as centre and taking convenient radius, draw two arcs that intersect ML produced at A and B.
(xi) With A as centre and taking radius more than half of AB, draw an arc. With B as centre and taking same radius, draw another arc that intersect the previous arc at C.
(xii) Join NC that intersect ML produced at J. NJ is an altitude to the side ML produced.
Hence,△LMN is the required triangle in which the altitudes LI, MK and NJ to the sides MN, NL and ML respectively intersect at O.
The point O is the orthocentre of △LMN.
Steps of construction :
(i) Draw an obtuse angled △LMN.
(ii) With L as centre and taking convenient radius, draw two arcs that intersect MN at P and Q.
(iii) With P as centre and taking radius more than half of PQ, draw an arc. With Q as centre and taking same radius, draw another arc that intersect the previous arc at R.
(iv) Join LR than intersect MN at I. LI is an altitude the side MN.
(v) Extend NL to a point V.
(vi) With M as centre and taking convenient radius, draw two arcs that intersect NL produced at D and E.
(vii) With D as centre and taking radius more than half of DE, draw an arc. With E as centre and taking same radius, draw another arc that intersect the previous arc at F.
(viii) Join MF that intersect NL produced at K. MK is an altitude to side NL produced.
(ix) Extend ML to point U.
(x) With N as centre and taking convenient radius, draw two arcs that intersect ML produced at A and B.
(xi) With A as centre and taking radius more than half of AB, draw an arc. With B as centre and taking same radius, draw another arc that intersect the previous arc at C.
(xii) Join NC that intersect ML produced at J. NJ is an altitude to the side ML produced.
Hence,△LMN is the required triangle in which the altitudes LI, MK and NJ to the sides MN, NL and ML respectively intersect at O.
The point O is the orthocentre of △LMN.
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