Q6 of 33 Page 40

Use a calculator to determine upto two decimal places, the perimeter and the area of the circle in the picture.

In the given fig, we can see, BC = 3cm and BD = 6cm


i. Join CD, thus we obtain a diameter CD.



ii. As ∠CBD = 90° (∵ angle in a semi circle is right angle)


Therefore by Pythagoras theorem


BC2 + BD2 = CD2


32 + 62 = CD2


CD2 = 9 + 36 =45


CD = 3√5


Thus, diameter = CD = 3√5


Radius,


iii. Now, change the position of a set square, and draw another diameter to get the center.



Thus, A is a centre.


Hence, radius,


We need to find perimeter of a circle?


We know that,


Perimeter of a circle = 2πr where r = radius



We need to find area of a circle?


We know that,


Area of a circle = π r2 where, r = radius




More from this chapter

All 33 →
4

In the picture, a circle is drawn with a line as diameter and a smaller circle with half the line as diameter. Prove that any chord of the larger circle through the point where the circles meet is bisected by the small circle.

 5

Prove that the two circles drawn on the two equal sides of an isosceles triangle as diameters pass through the midpoint of the third side.

 7

The two circles in the picture cross each other at A and B. The points P and Q are the other ends of the diameters through A.


i) Prove that P, B, Q lie on a line.


ii) Prove that PQ is parallel to the line joining the centres of the circles and is twice as long as this line.

 8

Prove that all four circles drawn with the sides of a rhombus as diameters pass through a common point.


Prove that this is true for any quadrilateral with adjacent sides equal, as in the picture.