Question

In a circle, the measure of an inscribed angle of an arc is 45°, find the ratio of length of the corresponding chord to that of the radius. (A) 1:2 (B) 2:1 ) √2 (C) 1:2 (D) 2:1​

Answer 1

Answer:

I think it's option B it is BBB option B BBB option B

Answer 2

given an arc's inscribed angle $45$ degrees , find the ratio of length of corresponding chord to radius  

Explanation:

1. here the chord forms an isosceles triangle in the arc, let it be named AOB.

2. in this triangle O is the center of the circle from which the arc is derived

   and edge AB is the chord corresponding the $45$° angle and let its

   length be l.

3.hence, the edges OB and OA are the radius therefore being the equal

  sides of the said isosceles triangle,$OB=OA=r$.

4. we have angle at vertex $O= 45$° and let there be a perpendicular line  

   OM bisecting angle O.

5. hence in triangles AOM and BOM we have,  

                              ∠  $AOM=BOM$$=\frac{45}{2}=22.5$°  

                                  $AM=BM=\frac{l}{2}\ and\ AO=BO=r$  

6. in triangle AOM we have,    $sin(AOM)=sin(22.5)= \frac{l}{2r}$      

                                                   $\frac{l}{r} =\sqrt{2-\sqrt{2} } \ \ \ \ \ (sin(22.5)=\frac{\sqrt{2-\sqrt{2} }}{2} )$  

7. hence the ration of length of chord to radius is $\sqrt{2-\sqrt{2} }:1$