Test: Triangles- Assertion-Reason & Case Base Type Questions - Class 9 MCQ

PQ = PR (Given)

QS = TR (Given)

∠PQR =∠PRQ (corresponding angles of an isosceles ∆)

By S AS congmency

∆PQS ≅ ∆PRT

In ∆ PQR, ∠P + ∠Q + ∠R = 180° (Angle sum property of ∆)

80° + x + x = 180°

2x = 180° – 80

2x = 100°

x = 100°/2 = 50°

PQ = PR = 6 cm,

QR = 7 cm

So P = (6 + 6 + 7) cm

= 19 cm

In the question, we have to check that the Statement 1: In triangle ABC, the centroid (G) divides the line joining orthocentre (O) and circumcentre (C) in ratio 2 : 1, is true or not and also we have to check that Statement 2: The centroid (G) divides the median AD in ratio 2 : 1, is correct or not. Finally, we have to check if statement 2 is the explanation of statement 1 or not.
So, here we know that In triangle ABC, the centroid (G) divides the line joining orthocentre (O) and circumcentre (C) in ratio 2 : 1. Also, we know that The centroid (G) divides the median AD in ratio 2 : 1. But the explanation given in statement 2 is not the correct reason for the statement 1 to be true.
So, from this we can say that option B, which says that Both the statements are TRUE but STATEMENT 2 is NOT the correct explanation of STATEMENT 1 is the correct answer.
Hence, option B is the correct answer.