Mathematics
The radius of a circle is 13 cm and length of chord is 10 cm. The shortest distance between chord and the centre is:
12 cm
15 cm
16 cm
18 cm
Circles
3 Likes
Answer
Let AB be chord of length = 10 cm
Radius OA = 13 cm
Let OD be the perpendicular distance from the center to the chord, it bisects the chord into two equal parts:
AD = DB = = 5 cm
In triangle OAD,
According to the Pythagorean Theorem:
OA2 = OD2 + AD2
132 = OD2 + 52
169 = OD2 + 25
OD2 = 169 - 25
OD2 = 144
OD = = 12 cm
The shortest distance between the chord and the center is 12 cm.
Hence, option 1 is the correct option.
Answered By
1 Like
Related Questions
Assertion (A): Equal chords of a circle subtend equal angles at the centre of the circle.
Reason (R): One and only one circle can be drawn passing through three points.
A is true, R is false
A is false, R is true
Both A and R are true
Both A and R are false
Two chords of a circle of lengths 10 cm and 8 cm are at the distances of 6 cm and 5 cm respectively from the centre. This statement is :
True
False
Can't say anything
Data inadequate
In the circle, chord AB of length 12 cm is bisected by diameter CD at P, so that CP = 3 cm. Radius of the circle is:
5.2 cm
6.5 cm
7.5 cm
8.3 cm
Three friends Amit, Vinay and Sukrit are playing a game by standing on a circle of radius 5 m drawn in a park. Amit throws a ball to Vinay, Vinay to Sukrit, Sukrit to Amit. If the distance between Amit and Vinay and between Vinay and Sukrit is 6 m each, what is the distance between Amit and Sukrit?