In Fig. 5.50, OB is perpendicular to OA and `angleBOC = 49^(@)`. Find `angleAOD.`

In Fig. 5.49, AB||CD, AF||ED, angleAFC = 68^(@) and angleFED = 42^(@) . Find angleEFD .

The resultant of vectors vec(OA) and vec(OB) is peerpendicular to vec(OA). Find the angle AOB.

In the given diagram ABCD is a cyclic quadrilateral angleOCB = 50 ^(@) and angleBOC = 110^(@) Find the value of angleDAO :

Two lines AB and CD intersect at O. If angleAOC=50^(@) , find angleAOD, angleBOD and angleBOC .

In the Fig. given below, OB is the perpendicular bisector of the line segment DE, FA bot OB and FE intersects OB at the point C. Prove that 1/(OA) + 1/(OB) = 2/(OC)

In Fig. 12.55, AB and CD are two perpendicular diameters of a circle with centre O. If OA= 7 cm, find the area of the shaded region. ("Use "pi=(22)/(7)) .

In Figure,OA and OB ar respectively perpendiculars to chords CD and EF of a circle whose centre is O. If OA=OB, prove that CE=DF.

The diagonals of a rectangle ABCD meet at O. If angleBOC=50^(@) then find angleODA .

An object is placed at A(OA gt f) . Here, f is the focal length of the lens. The image is formed at B. A perpendicular is erected at O and C is chosen such that /_BCA = 90^(@) . Let OA = a, OB = b and OC = c. Then the value of f is