If A, B, C, D are four points such that ∠BAC = 30° and ∠BDC = 60°, then D is the centre of the circle through A, B and C. Is the given statement true or false and justify your answer

Solution:

It is given that

A, B, C, D are four points

∠BAC = 30°

∠BDC = 60°

D is the centre of the circle through A, B and C

We know that

There can be many points D such that ∠BDC = 60° and each point cannot be the centre of the circle through A,B,C.

Therefore, the statement is false.

✦ Try This: If A, B, C, D are four points such that ∠BAC = 40° and ∠BDC = 70°, then D is the centre of the circle through A, B and C.

☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 10

NCERT Exemplar Class 9 Maths Exercise 10.2 Problem 8

If A, B, C, D are four points such that ∠BAC = 30° and ∠BDC = 60°, then D is the centre of the circle through A, B and C. Is the given statement true or false and justify your answer

Summary:

The statement “If A, B, C, D are four points such that ∠BAC = 30° and ∠BDC = 60°, then D is the centre of the circle through A, B and C” is false

☛ Related Questions:

• If A, B, C and D are four points such that ∠BAC = 45° and ∠BDC = 45°, then A, B, C, D are concyclic. . . . .
• In Fig. 10.10, if AOB is a diameter and ∠ADC = 120°, then ∠CAB = 30°. Is the given statement true or . . . .
• In Fig. 10.11, AOC is the diameter of the circle and arc AXB = 1/2 arc BYC. Find ∠BOC