Question

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

Answer 1

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

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 ]

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

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

$\textbf{Have great future ahead!}$