Areas Related to Circles

Question

Construct a ΔABC in which CA = 6 cm, AB = 5 cm and ∠BAC = 45°, then construct a triangle similar to the given triangle whose sides are 6/5 of the corresponding sides of the ΔABC.

Solution

Steps of Construction :
1.    Draw a line segment AB = 5 cm.
2.    At A make ∠BAY = 45°.
3.    Take A as centre and radius = AC = 6 cm (= CA), draw an arc cutting AY at C.
4.    Join BC to obtain the triangle ABC.
5.    Draw any ray AX making an acute angle with AB on the side opposite to the vertex
C.
6.    Mark off 6 points (the greater of 6 and 5 in 6/5) A₁, A₁, A₃, A₄,A₅ and A₆ on AX so
that
AA₁ = A₁A₂ = A₂A₃ = A₃A₄ = A₄A₅ = A₅A₆7.    Join A₅ (the 5th point, being the smaller of 5 and 6 in 5/6) to B and draw a line through A₆ parallel to A₅B intersecting the extended line segment AB at B’.
8.    Draw a line through B‘C’ parallel to BC intersecting the extended line segment AC at C’.
Thus, AB ‘C’ is the required triangle

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Construct a ΔABC in which CA = 6 cm, AB = 5 cm and ∠BAC = 45°, then construct a triangle similar to the given triangle whose sides are 6/5 of the corresponding sides of the ΔABC.

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Areas Related To Circles

Construct a ΔABC in which CA = 6 cm, AB = 5 cm and ∠BAC = 45°, then construct a triangle similar to the given triangle whose sides are 6/5 of the corresponding sides of the ΔABC.

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