Question

Q.5) Given is the centre of the circle and ZAOB = 70“,
Find () angle OCA, (ii) angle OAC.​

Answer 1

Property:

1. A Chord/arc of a circle subtends equal angles on same side of circumference (angles should be on same side)

2. Angle subtended by a chord/arc at centre is double the angle subtended by the same chord/arc at any point on circumference (both angles should be on same side)

Though not given in question, I am assuming that BC is a line, otherwise the problem won't solve.

now

Arc AB subtends angle AOB at centre and angle ACB at circumference on same side.

thus angle AOB = 2* angle ACB

2 angle ACB = 70°

angle ACB = 70°/2

angle ACB = 35°

again in ∆ AOC,

OA = OC (radius)

angle OCA = angle OAC

angle OCA = 35°

ALTERNATE METHOD

given,

angle AOB = 70°

now in ∆ AOC

OA = OC (radii)

<OCA = < OAC = x (let)

x + x = 70° ( <AOB is exterior angle = sum of interior opposit angles)

2x = 70°

x = 35°

so,

< OCA = < OAC = 35°