if DE and DF are tangents from an external point D to a circle with centre A. if De =5cm and DE perpendicular to DF, then the radius of the circle is .......
Answers
Answered by
97
Given : DE and DF are perpendicular to each other. DE= 5 cm. DE and DF are tangents to the circle with centre A.
Now since DE and DF are tangents to the circles
DE⊥ AE and DF ⊥ AF. ( The tangent at any point of a circle is perpendicular to the radius through the point of contact )
All the four angles of the quadrilateral AEFD are of 90°.Therefore AEFD is a rectangle.
And since opposite sides of arectangle are equal.
∴ AF = ED = 5cm = radius
Hence radius of the circle is 5 cm.
Now since DE and DF are tangents to the circles
DE⊥ AE and DF ⊥ AF. ( The tangent at any point of a circle is perpendicular to the radius through the point of contact )
All the four angles of the quadrilateral AEFD are of 90°.Therefore AEFD is a rectangle.
And since opposite sides of arectangle are equal.
∴ AF = ED = 5cm = radius
Hence radius of the circle is 5 cm.
Answered by
9
Answer:
5 cm
Step-by-step explanation:
i hope this will help you
Similar questions