The point where three medians of a triangle meet is called
Centroid
Incentre
Circumcentre
Orthocentre
Δ ABC a right-angled triangle has ∠B = 90° and AC is hypotenuse. D is its circumcentre and AB = 3 cm, BC = 4 cm. The value of BD is:
3 cm
4 cm
2.5 cm
5.5 cm
Δ ABC a right-angled triangle and D, E are midpoints of AB and BC respectively. Then the ratio of the area of Δ ABC and the area of trapezium ADEC is:
5 : 3
4 : 1
8 : 5
4 : 3
D.
4 : 3
By mid-point theorem:
area (Δ ABC) = ar (Δ ADF) = 1 : 1/4
Also,
ar (Δ ADF) = ar(Δ DFE) = ar(Δ EFC) = 1/4
ar(trapezium) = 1/4 + 1/4 + 1/4 = 3/4
∴ ar (Δ ABC) : ar (trapezium ADEC) = 1 : 3/4 = 4 : 3
In an isosceles triangle ABC, AB = AC, XY || BC. If ∠A = 30°, then ∠BXY = ?
75°
30°
150°
105°