ABCD is a cyclic quadrilateral in which AC and BD are its diagonals. If angleDBC = 55° and angle BAC = 45°, find BCD.
If two circles intersect at two points, then prove that their centres lie on the perpendicular bisector of the common chord.
ABC is a right angle triangle, right angled at A. A circle is inscribed in it. The length of two sides containing angle A is 12cm and 5cm find the radius.
ABC and ADC are two right triangles with common hypotenuse AC. Prove that ∠CAD = ∠CBD.
In a circle with centre O,chords AB and CD intersect inside the circumference at E.Prove that ∠AOC + ∠BOD = 2∠AEC
OD is perpendicular to chord AB of a circle whose centre is O. if BC is a diameter prove that CA=2OD
in the figure, chord AB of circle with centre O, is produced to C such that BC = OB . CO is joined and produced to meet the circle at D.If angle ACD = y and angle AOD = x,show that x = 3y.
AB and AC are two chords of a circle of radius r such that AB = 2AC. if p and q are distances of AB and AC from the centre , prove that 4q2 = p2 = 3r2
X &Y are centres of circles of radius 9cm, 2cm and XY=17cm.Z is the centre ofcircle of radius r cm, which touches the above circle externally given that XZY=90degree. Write an equation inr and solve it for r
If two sides of a cyclic quadrilateral are parallel , prove tha the remaining two sides are equal and the diagonals are also equal
Two congruent circles intersect each other at points A and B. Through A any line segment PAQ is drawn so that P, Q lie on the two circles. Prove that BP = BQ.
if two intersecting chords of a circle make equal angles with the diameter passing through their point of intersection , prove that the chords are equal.
Two circles whose centres are O and O' intersect at P. Through P, line "l" parallel to OO' intersecting the circles at C and D is drawn. Prove that CD=2OO'.
If diagonals of a cyclic quadrilateral are diameters of the circle through the vertices of the quadrilateral, prove that it is a rectangle.
an equilateral triangle of side 9 cm is inscribed in a circle.Find the radius of the circle
ABCD is a cyclic quadrilateral in which AC and BD are its diagonals. If angleDBC = 55° and angle BAC = 45°, find BCD.
If two circles intersect at two points, then prove that their centres lie on the perpendicular bisector of the common chord.
ABC is a right angle triangle, right angled at A. A circle is inscribed in it. The length of two sides containing angle A is 12cm and 5cm find the radius.
ABC and ADC are two right triangles with common hypotenuse AC. Prove that ∠CAD = ∠CBD.
In a circle with centre O,chords AB and CD intersect inside the circumference at E.Prove that ∠AOC + ∠BOD = 2∠AEC
OD is perpendicular to chord AB of a circle whose centre is O. if BC is a diameter prove that CA=2OD
in the figure, chord AB of circle with centre O, is produced to C such that BC = OB . CO is joined and produced to meet the circle at D.If angle ACD = y and angle AOD = x,show that x = 3y.
AB and AC are two chords of a circle of radius r such that AB = 2AC. if p and q are distances of AB and AC from the centre , prove that 4q2 = p2 = 3r2
X &Y are centres of circles of radius 9cm, 2cm and XY=17cm.Z is the centre ofcircle of radius r cm, which touches the above circle externally given that XZY=90degree. Write an equation inr and solve it for r
If two sides of a cyclic quadrilateral are parallel , prove tha the remaining two sides are equal and the diagonals are also equal
Two congruent circles intersect each other at points A and B. Through A any line segment PAQ is drawn so that P, Q lie on the two circles. Prove that BP = BQ.
if two intersecting chords of a circle make equal angles with the diameter passing through their point of intersection , prove that the chords are equal.
Two circles whose centres are O and O' intersect at P. Through P, line "l" parallel to OO' intersecting the circles at C and D is drawn. Prove that CD=2OO'.
If diagonals of a cyclic quadrilateral are diameters of the circle through the vertices of the quadrilateral, prove that it is a rectangle.
an equilateral triangle of side 9 cm is inscribed in a circle.Find the radius of the circle