Advertisements
Advertisements
Question
A chord of length 14 cm is at a distance of 6 cm from the centre of a circle. The length of another chord at a distance of 2 cm from the centre of the circle is
Options
12 cm
12 cm
12 cm
18 cm
Advertisements
Solution
18 cm
We are given the chord of length 14 cm and perpendicular distance from the centre to the chord is 6 cm. We are asked to find the length of another chord at a distance of 2 cm from the centre.
We have the following figure
We are given AB = 14 cm, OD = 6 cm, MO = 2 cm, PQ = ?
Since, perpendicular from centre to the chord divide the chord into two equal parts
Therefore
`AQ^2 = AD^2 +OD^2`
= ` 7^2 + 6^2`
= 49 + 36
`= sqrt( 85)`
Now consider the ΔOPQ in which OM = 2 cm
So using Pythagoras Theorem in ΔOPM
`PM^2 = OP^2 -OM^2`
`=(sqrt(85))^2 - 2^2` (∵ OP = AO = radius)
= 81
= 9 cm
Hence PQ = 2 PM
= 2 × 9
= 18 cm
APPEARS IN
RELATED QUESTIONS
In Fig. 2, AB is the diameter of a circle with centre O and AT is a tangent. If ∠AOQ = 58°, find ∠ATQ.
In the given figure, PQ and RS are two parallel tangents to a circle with centre O and another tangent AB with point of contact C intersects PQ at A and RS at B. Prove that ∠AOB = 90º
In the given figure, O is the centre of a circle. PT and PQ are tangents to the circle from an external point P. If ∠TPQ = 70° , find the ∠TRQ.
If the area of a circle is equal to sum of the areas of two circles of diameters 10 cm and 24 cm, then the diameter of the larger circle (in cm) is:
In the given figure, two tangents AB and AC are drawn to a circle with centre O such that ∠BAC = 120°. Prove that OA = 2AB.
In the given figure, BC is a tangent to the circle with centre O. OE bisects AP. Prove that ΔAEO ∼ Δ ABC.
Use the figure given below to fill in the blank:
________ is a radius of the circle.
Draw circle with the radii given below.
3 cm
Three circles touch each other externally. The distance between their centres is 5 cm, 6 cm, and 7 cm. Find the radii of the circles.
In figure, tangents PQ and PR are drawn to a circle such that ∠RPQ = 30°. A chord RS is drawn parallel to the tangent PQ. Find the ∠RQS.
[Hint: Draw a line through Q and perpendicular to QP.]
