Question

to prove that the segments joining the center af a circle and mid point of its chord is perpendicular to chord 1)draw a neat labbleed figure 2)write given and prove guys plz tell me answers​

Answer 1

The line segments joining the center of a circle and mid point of its chord is perpendicular to chord

• Given OP is the segment joining center of the circle and midpoint of its chord AB.

Consider triangles OAP and OBP.

• OA = OB= radius of the circle.

• OP =OP, common side

• AP = BP, its given OP bisects AB.

• by SSS congruence rule, Triangles OAP and OBP are congruent.

Hence Angles <OPB and <OPA are equal.

We know,

• sum of angles OPB and OPA are 180 degree, since AB is a straight line.

• Hence <OPB + <OPA  = 2<OPB = 180 degree.

• <OPB = <OAB = 90 degree.

Hence, the segment joining the center of a circle and mid point of its chord is perpendicular to chord