Q7 of 141 Page 400

In the given figure, a circle with center is given in which a diameter bisects the chord at a point such that and Find the radius of the circle.

Let radius OA = OB = OD = r


DE = 8 cm


OE = OB – BE


⇒ OE = r – 4



In triangle ODE,


OD2 = DE2 + OE2


⇒ r2 = 82 + (r - 4)2


⇒ r2 = 64 + r2 + 16 - 8r


⇒ 8r = 80


⇒ r = 10 cm


Hence, radius of circle = 10 cm.


More from this chapter

All 141 →
5

Two parallel chords of lengths 30 cm and 16cm are drawn on the opposite sides of the center of a circle of radius 17 cm. Find the distance between the chords.

 6

In the given figure, the diameter of a circle with center is perpendicular to chord If and calculate the radius of the circle.

 8

In the adjoining figure, is perpendicular to the chord of a circle with center If is a diameter, show that and

9

In the given figure, is the center of a circle in which chords and intersect at such that bisects Prove that