Question

In the figure find the length of an arc AB of a circle centre O if AOB = 90^o

Answer 1

Answer:(1) In the given figure, OA and OB are the radii of the circle. OA=OB=AB (Given) ∴△OAB is an equilateral triangle. ⇒∠AOB=∠OAB=∠OBA=60 o Thus, the measure of ∠AOB is 60 o . (2) The measure of an angle subtended by an arc at a point on the circle is half of the measure of the angle subtended by the arc at the centre. ∠ACB= 2 1 ​ ∠AOB= 2 1 ​ 60o=30 o Thus, the measure of ∠ACBis30 o . (3) m(arcAB)=∠AOB=60 o (Measure of an arc is the measure of its corresponding central angle) Thus, the measure of arc AB is 60 o . (4) m(arcACB)=360 o - m(arcAB)=360 o −60 o =300 o Thus, the measure of arc ACB is 300 o .

Answer 2

Given:

Angle AOB = 90°

To find:

Length of the arc AB

Solution:

The required length is 11 cm.

We can obtain the length by using the following formula as it forms a part of the circle's circumference.

The required length of the arc=Angle AOB/360°×2πR

The circle's radius=R=7 cm

Using the values, we get

The required length of the arc=90°/360°×2×22/7×7

=1/4×44

=44/4

=11 cm

Therefore, the required length is 11 cm.