In triangle ABC a straight line parallel to BC intersects AB and AC at D and E respectively. If AB = 2AD then DE : BC is

ABCD is a cyclic quadrilateral and AD is a diameter. If ∠DAC=55° then value of ∠ABC is

If the area of a circle, inscribed in a equilateral triangle is 4 π cm², then what is the area of the triangle?

∆ABC is a right angle triangle BD⊥AC. If AD = 12 cm and DC = 8, then BD = ?

Line 2x + y = 3 and 3x - 2y = 1 meets X-axis at two two points. Find the distance between these points.

X and Y are centres of circles of radius 9 cm. and 2 cm respectively XY=17 cm. Z is the centre of a circle of radius r cm which touches the above circles externally. Given that - ∠xzy = 90^o the value of r is -

In ΔABC, ∠C=90° and D is a point on CB such that AD is the bisector of ∠A. If AC=5 cm and BC=12 cm, then what is the length of AD?

ABCD is cyclic quadrilateral Sides AB and DC, when produced, meet at E, and sides BC and AD, When produced, meet at F. If ∠BFA=60° and ∠AED=30°, then the measure of ∠ABC is: