Q5 of 26 Page 230

Prove that the tangents to a circle at the end points of a diameter are parallel.


To prove: DE ∥ FG


Proof:


We know that tangent to a circle makes a right angle with the radius.


Let DE and FG be tangent at B and C respectively.


BC forms the diameter.


∴ ∠OBE = ∠OBD = ∠OCG = ∠OCF = 90°


Also, ∠OBD = ∠OCG and ∠OBE = ∠OCF as alternate angles


∴ DE and FG make 90° to same line BC which is the diameter.


Thus DE ∥ FG


More from this chapter

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3

Draw a circle and two lines parallel to a given line such that one is a tangent and the other, a secant to the circle.

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Calculate the length of tangent from a point 15 cm. away from the circle of a circle of radius 9 cm.

 1

Choose the correct answer and give justification for each.

The angle between a tangent to a circle and the radius drawn at the point of contact is


A. 60o


B. 30o


C. 45o


D. 90o

 1

Choose the correct answer and give justification for each.

From a point Q, the length of the tangent to a circle is 24 cm. and the distance of Q from the centre is 25 cm. The radius of the circle is


A. 7 cm


B. 12 cm


C. 15 cm


D. 24.5 cm