The area of the triangle formed by the lines 5x + 7y = 35, 4x + 3y = 12 and x-axis is
160/13 sq units
150/13 sq units
140/13 sq units
10 sq units
In an obtuse-angled triangle ABC, ∠A is the obtuse angle and O is the orthocentre. If ∠BOC = 54°, then ∠BAC is
108°
126°
136°
116°
If the ratio of area of two similar triangles is 9 : 16, then the ratio of their corresponding sides is
3 : 5
3 : 4
4 : 5
4 : 3
Let BE and CF be the two medians of a Δ ABC and G be their intersection. Also let EF cut AG at O. Then, AO : OG is
1 : 1
1 : 2
2 : 1
3 : 1
D.
3 : 1
Extend AG to cut BC at D
E and F are midpoints, hence EF=1/2BC
Triangles AFO and ABD are similar
OF/BD = OA/AD
Now OF/BD = 1/2
Hence OA/AD = 1/2
∴ O will be the mid-point of AD i.e AO = OD
Now,
As centroid divides the median in the ratio of 2 : 1
∴ AO : OG = 3 : 1
If S is the circumcentre of Δ ABC and ∠A = 50° then the value of ∠BCS is
20°
40°
60°
80°
AC and BC are two equal chords of a circle. BA is produced to any point P and CP, when joined cuts the circle at T. Then,
CT : TP = AB : CA
CT : TP = CA : AB
CT : CB = CA : CP
CT : CB = CP : CA