Worksheet title

ABC is a right triangle(A=90) whose 3 vertices lie on a circle of diameter 10cm if the area of the triangle is 25 sq.cm then which among the following is false?

• The triangle is isosceles
• the perpendicular bisector of AB passes through C
• The orthocenter, circumcenter of ABC and the perpendicular bisector of BC are collinear
• square of the side AC is 50 units.

4 equal chords are drawn in a circle then which of the following is always true about the midpoints of those chords.

• they form a rectangle
• they form a parrallelogram
• they form a cyclic quadrilateral
• they form a trapezium

AB is a chord of the circle whose center is O, radius = 8cm and the midpoint of the chord AB is D if angle ABO is 60 then the value of OD is

• root(46)
• root(60)
• root(48)
• root(52)

Consider a circle with center O, radius=6cm and a chord AB, whose midpoint is D of the circle which among the following is true ?

• if angle OAB > 45 then AB can be 9cm
• if angle OAB < 60 then AB can be 5cm
• if angle OAB < 30 then AB can be 4cm
• if angle OAB<45 then AB can be 10cm

IF ABCD is a trapezium such that interior angle A + angle D = 180 and AD = BC = 6cm. If interior angle C is 70 then interior angle A is

• 60
• 70
• 110
• 50

Two circles of radii 9cm and 12cm are drawn such that the common chord drawn through their point of intersection has a length of 18cm then the distance between their centers is?

• 15cm
• 14cm
• 18cm
• 16cm

which of the following is false in an equilateral triangle?

• the circumcenter and the orthocenter coincide
• the circumcenter and the centroid coincide
• the centroid divides the altitude through any vertex in the ratio 2:1
• If AB s a side of the triangle and O is it's orthocenter then angle AOB is 60

Chords AB and CD of a circle intersect at E, then which of these is true?

• chords AD and CB are equal always
• AC = DB only if AB and CD intersect at the center
• if AB = CD then AD equal to CB
• None of these

If the exterior angle of a quadrilateral is equal to it's interior opposite angle then the quadrilateral must be

• cyclic
• rectangle
• parallelogram
• rhombus

If in a cyclic quadrilateral adjacent angles are supplementary then which of the following is surely true?

• it is a rhombus
• it is a rectangle
• it is a square
• it is parallelogram only and no additional details could be said