The angles subtended by a chord at any two points of a circle are equal. Is the given statement true or false and justify your answer
Solution:
If two points lie in the same segment then only the angles will be equal otherwise not.
The two points that lie ONLY in the same major segment or the same minor segment, the angles subtended by the chord at those points will be equal.
Therefore, the statement is false.
✦ Try This: If AB = 6 cm, BC = 8 cm and AB is perpendicular to BC, then the radius of the circle passing through the points A, B and C is:
It is given that
AB = 6 cm
BC = 8 cm
In the circle, BC is perpendicular to AB which means that AC is the diameter
In triangle ABC,
Using the Pythagoras theorem
AC² = AB² + BC²
Substituting the values
AC² = 6² + 8²
By further calculation
AC² = 36 + 64
AC² = 100
So we get
AC = 10 cm
We know that
Radius of circle = 1/2 AC
= 1/2 × 10
= 5 cm
Therefore, the radius of the circle is 5 cm.
☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 10
NCERT Exemplar Class 9 Maths Exercise 10.2 Sample Problem 1
The angles subtended by a chord at any two points of a circle are equal. Is the given statement true or false and justify your answer
Summary:
The statement “The angles subtended by a chord at any two points of a circle are equal” is false
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