Question

In triangle PQR ,QT and RS are medians intersecting at G.prove that triangle SGT similar to triangle QGT.

Answer 1

hope my answer will help you

Answer 2

Answer:

OM = ON is proved

Step-by-step explanation:

Given:   ON ⟂ AB and OM ⟂ CD

Construction: Join OD and OC. Join OA and OB.

IMG

Solution:

Concept: “Perpendicular bisects the chords into two equal halves”

              OA = OC                 (Radius of circles)

              OB = OD                (Radius of circles)  

AB and CD are equal chords, therefore

               CD = AB                 (Equal chords have equal distance from the centre)

               CM = ½ CD                 (Perpendicular bisects the chords into two equal halves)

               CM = OM

               2AN = ½ AB                (Perpendicular bisects the chords into two equal halves)

                  AN = BN

         AN + BN = CM + DM

         AN + AN = CM +CM

               2 AN = 2 CM

                   AB = CD

Therefore,

                  OA = OC

                  OB = OD

                   AB = CD                 (by SSS rule congruency, △AOB ≅ △COD)

           ∠ OMN = ∠ ONM

                 OM = ON

Hence Proved.