Question

Prove that the angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circle

Answer 1

hence it is prove that the angle subtended by an arc at the center is double the angle subtended by it at any point on the remaining part of the circle

Answer 2

$\textsf{\huge{\underline{Hello Mate!}}}$

Given : PQ is a chord where (i) PQ is minor arc, (ii) PQ is semicircular arc and (iii) PQ is major arc.

To prove : < POQ = 2 < PRQ.

To construct : Extend OR passing through center of circle.

Proof : Please refer to attachment above.

Concept used : Exterior angle property whivh states that sum of two interior opposite angle is equal to one exterior angle.

Mathematically, ext. < = opp. [ < interior + < interior ]

$\textsf{\red{Hence proved.}}$

$\textbf{\large{Q.E.D}}$

$\textbf{Have great future ahead!}$