If A, B, C and D are four points such that ∠BAC = 45° and ∠BDC = 45°, then A, B, C, D are concyclic. Is the given statement true or false and justify your answer

Solution:

It is given that

A, B, C and D are four points

∠BAC = 45°

∠BDC = 45°

We have to find if the points are concyclic

Consider the figure

We know that

Angles in the same segment of a circle are equal

So A, B, C and D are concyclic.

Therefore, the statement is true.

✦ Try This: If A, B, C and D are four points such that ∠BAC = 35° and ∠BDC = 55°, then A, B, C, D are concyclic.

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

NCERT Exemplar Class 9 Maths Exercise 10.2 Problem 9

If A, B, C and D are four points such that ∠BAC = 45° and ∠BDC = 45°, then A, B, C, D are concyclic. Is the given statement true or false and justify your answer

Summary:

The statement “If A, B, C and D are four points such that ∠BAC = 45° and ∠BDC = 45°, then A, B, C, D are concyclic” is true

☛ Related Questions:

• 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
• In Fig. 10.12, ∠ABC = 45º, prove that OA ⊥ OC