Advertisements
Advertisements
Question
If the length of a chord of a circle is 16 cm and is at a distance of 15 cm from the centre of the circle, then the radius of the circle is
Options
15 cm
16 cm
17 cm
34 cm
Advertisements
Solution
17 cm
We will represent the given data in the figure
In the diagram AB is the given chord of 16 cm length and OM is the perpendicular distance from the centre to AB.
We know that perpendicular from the centre to any chord divides it into two equal parts.
So, AM = MB = `16/2` = 8 cm.
Now consider right triangle OMA and by using Pythagoras theorem
`AO^2 = AM^2 + OM^2`
`= 8^2 + 15^2`
= 64+225
= 289
`= sqrt(289)`
= 17 cm
APPEARS IN
RELATED QUESTIONS
If the tangent at point P to the circle with center O cuts a line through O at Q such that PQ= 24cm and OQ = 25 cm. Find the radius of circle
O is the centre of a circle of radius 10 cm. P is any point in the circle such that OP = 6 cm. A is the point travelling along the circumference. x is the distance from A to P. what are the least and the greatest values of x in cm? what is the position of the points O, P and A at these values?
In the adjoining figure, a circle touches all the four sides of a quadrilateral ABCD whose sides are AB = 6 cm, BC = 9 cm and CD = 8 cm. Find the length of side AD.
In Fig. 4, an isosceles triangle ABC, with AB = AC, circumscribes a circle. Prove that the point of contact P bisects the base BC.
In Fig. 5, the chord AB of the larger of the two concentric circles, with centre O, touches the smaller circle at C. Prove that AC = CB.
In the given figure, BDC is a tangent to the given circle at point D such that BD = 30 cm and CD = 7 cm. The other tangents BE and CF are drawn respectively from B and C to the circle and meet when produced at A making BAC a right angle triangle. Calculate (i) AF
If O is the centre of the circle, find the value of x in each of the following figures
The longest chord of a circle is __________
In the figure, O is the center of the circle. Line AQ is a tangent. If OP = 3, m(arc PM) = 120°, then find the length of AP.
In the given figure, if ZRPS = 25°, the value of ZROS is ______
