Advertisements
Advertisements
Question
In figure ∠ABC = 120°, where A, B and C are points on the circle with centre O. Find ∠OAC?
Solution
Reflex ∠AOC = 2∠ABC
= 20 × 120°
= 240°
∴ ∠AOC = 360° – 240°
= 120°
∠OCA + ∠OAC = 180° – 120°
= 60°
∴ ∠OAC = `60/2`
= 30° ...(Since OA = OC)
APPEARS IN
RELATED QUESTIONS
Show that ABCD is a parallelogram if A = (4, 8), B = (5, 5), C = (2, 4), D = (1, 7)
If P(-2,4), Q(4,8), R(10, 5) and S(4, 1) are the vertices of a quadrilateral, show that it is a parallelogram.
`square`ABCD is cyclic. If ∠B = 110°, then find measure of ∠D.
In figure, points G, D, E, F are concyclic points of a circle with centre C.
∠ECF = 70°, m(arc DGF) = 200°
Find m(arc DEF) by completing activity.
m(arc EF) = ∠ECF ......[Definition of measure of arc]
∴ m(arc EF) = `square`
But; m(arc DE) + m(arc EF) + m(arc DGF) = `square` .....[Measure of a complete circle]
∴ m(arc DE) = `square`
∴ m(arc DEF) = m(arc DE) + m(arc EF)
∴ m(arc DEF) = `square`
Two opposite angles of a parallelogram are (2x + 60)° and (4x)°. Find the value of x.
