Q9 of 49 Page 1

Two concentric circles are of radii 7 cm and r cm respectively, where r > 7. A chord of the larger circle of length 48 cm, touches the smaller circle. Find the value or r.


The angle between tangent and radius is 90°.
∴ ∠ OCA=90°


Also ∠OCB=90°


⇒ OC ⊥ AB


AC=1/2 AB(Perpendicular from center bisects chord(AB) of the circle)


∴ AC= 1/2 (48)=24cm


Now we consider the right-angled triangle OAC,


(OA)2=(OC)2 + (AC)2


(r)2=(7)2 + (24)2 =625


r=√ 625 =25cm


More from this chapter

All 49 →
7

Find the value of p so that the quadratic equation px(x – 3) + 9 = 0 has two equal roots.

 8

Find whether -150 is a term of the A.P. 17, 12, 12, 7, 2, ….?

 10

Draw a line segment 6 cm. Using compasses and ruler, find a point P on it which divides it in the ratio 3: 4.

 11

In Fig. 3, APB and CQD are semi-circles of diameter 7 cm each, while ARC and BSD are semi-circles of diameter 14 cm each. Find the perimeter of the shaded region.

Or


Find the area of a quadrant of a circle, where the circumference of a circle is 44 cm.