An arc AB forms $∠ A O B$ at the centre of the circle. If we draw 2 arcs with A and B as centre and a fixed radius 'r' such that they intersect at point P. The line OP will ___________ the $∠ A O B$ .

be at right angles to

No worries! We‘ve got your back. Try BYJU‘S free classes today!

bisect

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

trisect

No worries! We‘ve got your back. Try BYJU‘S free classes today!

be at zero angle to

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B
bisect

If we draw two arcs from any random points A and B with radius larger than half the distance between AB, the perpendicular bisector of AB passes through the point of intersection of the two arcs. If you consider the line AB to be a chord then the perpendicular of AB passing through centre will bisect the chord. By combining the two concepts we can arrive at the conclusion that the perpendicular passing through P and O bisects the arc AB. Therefore, OP will bisect the $∠ A O B$ .

Suggest Corrections

Similar questions

An arc ACB subtends $∠ A O B$ at the centre of the circle. If 2 arcs are drawn with A and B as centre with a fixed radius such that they intersect at point P, then line OP will ___________ $∠ A O B$ .

An arc AB forms $∠ A O B$ at the centre of the circle. If I draw 2 arcs with A and B as centre and a fixed radius 'r' such that they intersect at point P. The line OP will __ the $∠ A O B$ .

If I do the following constructions step by step, what will be the angles constructed (in degrees)?

Step 1. Draw an arc on the line XY with an arbitrary point O on line XY, as centre and radius r. With the same radius and point of intersection of arc and line, ‘A’, as centre draw another arc on the first arc at point B. So, $∠ A O B$ is __.

Pavan tried to draw a line parallel to a given line, 'l'. Few steps are shown below. What will be the next step?

Step 1: Mark a point A, not on the line 'l'.
Step 2: Mark point B on line 'l'.
Step 3: Draw line segment joining points A and B.
Step 4: Draw an arc with B as the centre, such that it intersects line 'l' at D and AB at E.

Step 4. Now, change the radius to R. Draw an arc such that it intersects line XY at E and line OD at F. Draw arcs with radius R and centres at E and F respectively such that they intersect at G. The $∠ G O E$ is __.
Note: Answer in degrees.

Join BYJU'S Learning Program

An arc AB forms ∠AOB at the centre of the circle. If we draw 2 arcs with A and B as centre and a fixed radius 'r' such that they intersect at point P. The line OP will ___________ the ∠AOB.

An arc AB forms $∠ A O B$ at the centre of the circle. If we draw 2 arcs with A and B as centre and a fixed radius 'r' such that they intersect at point P. The line OP will ___________ the $∠ A O B$ .