If AB = 12 cm, BC = 16 cm and AB is perpendicular to BC, then the radius of the circle passing through the points A, B and C is :
a. 6 cm
b. 8 cm
c. 10 cm
d. 12 cm
Solution:
It is given that
AB = 12 cm
BC = 16 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 = 12² + 16²
By further calculation
AC² = 144 + 256
AC² = 400
So we get
AC = 20 cm
We know that
Radius of circle = 1/2 AC
= 1/2 × 20
= 10 cm
Therefore, the radius of the circle is 10 cm.
✦ Try This: If AB = 14 cm, BC = 18 cm and AB is perpendicular to BC, then the radius of the circle passing through the points A, B and C is :
☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 10
NCERT Exemplar Class 9 Maths Exercise 10.1 Problem 3
If AB = 12 cm, BC = 16 cm and AB is perpendicular to BC, then the radius of the circle passing through the points A, B and C is : a. 6 cm, b. 8 cm, c. 10 cm, d. 12 cm
Summary:
If AB = 12 cm, BC = 16 cm and AB is perpendicular to BC, then the radius of the circle passing through the points A, B and C is 10 cm.
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