Q3 of 26 Page 235

Prove that the parallelogram circumscribing a circle is a rhombus.


FGHI is a parallelogram


∴ HI = FG and FI = GH----1


Also


IB = IE tangents to circle from I


And similarly


HE = HD, CG = GD and CF = BF


Adding all the equations


IE + HE + GC + CF = BF + BI + GD + DH


IH + GF = IF + GH


∴ 2HI = 2HG


HI = HG---2


∴ GF = GH = HI = IF


From 1 and 2


Thus FGHI is a rhombus


More from this chapter

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1

Choose the correct answer and give justification for each.

In the figure XY and X1Y1 are two parallel tangents to a circle with centre O and another tangent AB with point of contact C intersecting XY at A and X1Y1 at B then ∠AOB =



A. 80o


B. 100o


C. 90o


D. 60o

 2

Two concentric circles of radii 5 cm and 3 cm are drawn. Find the length of the chord of the larger circle which touches the smaller circle.

 4

A triangle ABC is drawn to circumscribe a circle of radius 3 cm. such that the segments BD and DC into which BC is divided by the point of contact D are of length 9 cm. and 3 cm. respectively (See adjacent figure). Find the sides AB and AC.

 5

Draw a circle of radius 6 cm. From a point 10 cm away from its centre, construct the pair of tangents to the circle and measure their lengths. Verify by using Pythogoras Theorem.