At one end A of a diameter AB of a circle of radius 5 cm, tangent XAY is drawn to the circle. The length of the chord CD parallel to XY and at a distance 8 cm from A is
a. 4 cm
b. 5 cm
c. 6 cm
d. 8 cm
Solution:
Given, AB is the diameter of a circle
Radius of the circle is 5 cm
At one end A of the circle, tangent XAY is drawn.
We have to find the length of the chord CD parallel to XY and at a distance 8 cm from A.
From the figure,
XAY is the tangent of the circle
CD is the chord
The distance of chord CD from A, AE = 8 cm
Radius, AO = OC = 5 cm
We know that AE = AO + OE
8 = 5 + OE
OE = 8 - 5
OE = 3 cm
We observe that OE is perpendicular to the chord CD.
So, ∠ OEC = 90°
We know that the perpendicular drawn from the centre to the chord bisects the chord.
i.e., CE = DE
In triangle OED,
OED is a right triangle with right angle at E.
OC² = OE² + CE²
(5)² = (3)² + CE²
CE² = 25 - 9
CE² = 16
Taking square root,
CE = 4 cm
Length of the chord CE = 2(CE)
= 2(4)
= 8 cm
Therefore, the length of the chord is 8 cm.
✦ Try This: PQ is a tangent drawn from a point P to a circle with centre O and QOR is a diameter of the circle such that ∠POR = 120° , then ∠OPQ is
☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 10
NCERT Exemplar Class 10 Maths Exercise 9.1 Problem 5
At one end A of a diameter AB of a circle of radius 5 cm, tangent XAY is drawn to the circle. The length of the chord CD parallel to XY and at a distance 8 cm from A is a. 4 cm, b. 5 cm, c. 6 cm, d. 8 cm
Summary:
At one end A of a diameter AB of a circle of radius 5 cm, tangent XAY is drawn to the circle. The length of the chord CD parallel to XY and at a distance 8 cm from A is 8 cm
☛ Related Questions:
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