Q7 of 100 Page 17

In Fig. 16.182, AB and CD are diameters of a circle with centre O. If ∠OBD=50°, find ∠AOC.

Given that,

∠OBD = 50o


Since,


AB and CD are the diameters of the circles and O is the centre of the circle


Therefore,


∠PBC = 90o (Angle in the semi-circle)


∠OBD + ∠DBC = 90o


50o + ∠DBC = 90o


∠DBC = 40o


By degree measure theorem,


∠AOC = 2 ∠ABC


∠AOC = 2 * 40o


= 80o


More from this chapter

All 100 →
5

If ABCD is a cyclic quadrilateral in which AD||BC (fig. 16.180). Prove that ∠B=∠C.

 6

In Fig. 16.181, O is the centre of the circle. Find ∠CBD.

 8

On a semi-circle with AB as diameter, a point C is taken, so that m(∠CAB)= 30°. Find m(∠ACB) and m(∠ABC).

 9

In a cyclic quadrilateral ABCD if AB||CD and B=70°, find the remaining angles.