In the given figure, ABC is a right angled triangle with AB = 16 cm and BC = 30 cm. A circle with centre O has been inscribed inside the triangle. Calculate the value of 'x', the radius of the inscribed circle.In the above figure, major arc ACB subtends an angle of 315° at the centre O of the circle. If the radius of the circle is 14 cm then find the area of the minor segment AB.
Answers
Answer:
In the given figure, ABC is a right angled triangle with AB = 16 cm and BC = 30 cm. A circle with centre O has been inscribed inside the triangle. Calculate the value of 'x', the radius of the inscribed circle.In the above figure, major arc ACB subtends an angle of 315° at the centre O of the circle. If the radius of the circle is 14 cm then find the area of the minor segment AB.
Step-by-step explanation:
Since AB,BC and CA are tangents to the circle
⇒ OP,OM and ON are radius of the incircle
To find : radius 'r' of the incircle.
ABC is a right angled triangle
AB
2
+AC
2
=BC
2
(Using pythagoras theorem)
⇒ (6)
2
+(8)
2
=BC
2
⇒ BC
2
=36+64
=100
⇒ BC=
100
=10cm
Since area of right anged triangle =
2
1
×base×height
⇒ Area of △ABC=
2
1
×6×8
=3×8=24cm
2
⇒ Area of △ABC=24cm
2
....(1)
Also, Area of △ABC= area of △OAC+ area of △OBC+ area of △OBA
=
2
1
×r×8+
2
1
×r×10+
2
1
×6×r=
2
1
r(8+10+6)=
2
1
r(24)=12r....(2)
Equating (1) and (2) 12r=24
⇒ r=
12
24
=2cm