The length of two chords AB and AC of a circle are 8cm and 6cm

Solution:

The perpendicular drawn from the center of the circle to the chords bisects it.

Draw two parallel chords AB and CD of lengths 6 cm and 8 cm. Let the circle's center be O. Join one end of each chord to the center. Draw 2 perpendiculars OM and ON to AB and CD, respectively, which bisects the chords.

AB = 6 cm CD = 8 cm MB = 3 cm ND = 4 cm

Given OM = 4 cm and let ON = x cm Consider ΔOMB

By Pythagoras theorem,

OM² + MB² = OB²

4² + 3² = OB²

OB² = 25

OB = 5 cm

OB and OD are the radii of the circle.

Therefore OD = OB = 5 cm.

Consider ΔOND

By Pythagoras theorem,

ON² + ND² = OD²

x² + 4² = 5²

x² = 25 - 16

x² = 9

x = 3

The distance of the chord CD from the center is 3 cm.

☛ Check: NCERT Solutions for Class 9 Maths Chapter 10

Video Solution:

The lengths of two parallel chords of a circle are 6 cm and 8 cm. If the smaller chord is at distance 4 cm from the center, what is the distance of the other chord from the centre?

Maths NCERT Solutions Class 9 Chapter 10 Exercise 10.6 Question 3

Summary:

The lengths of two parallel chords of a circle are 6 cm and 8 cm. If the smaller chord is at a distance of 4 cm from the center, we have found that the distance of the other chord CD from the center is 3 cm.

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Home » Aptitude » Plane Geometry » Question

The length of two chords AB and AC of a circle are 8 cm and 6 cm and ∠BAC = 90°, then the radius of circle is

According to question , we draw a figure of a circle with two chords AB and AC ,

Here , AB = 8 cm and AC = 6 cm∠ BAC = 90° As, BC is the diameter of the circle.

∴ BC = √AB² + AC²

BC = √8² + 6²
BC = √64 + 36
BC = √100 = 10 cm
∴ Radius of the circle = 5 cm

Correct Answer:

Description for Correct answer:

According to question,AB and AC are chordsAB = 8AC = 6

\( \Large In \triangle BAC \)\( \Large \angle A=90 ^{\circ}\)\( \Large \therefore BC^{2}=AB^{2}+AC^{2} \)\( \Large BC^{2}=8^{2}+6^{2} \)\( \Large BC^{2}=64+36 \)\( \Large BC^{2}=100 \)BC = 10 cmHere BC is the diameter of a circle because angle subtended on the arc of semi circle is \(90 ^{\circ}\)

\( \Large \therefore \frac{BC}{2}=radius=\frac{10}{2}=5cm \)

Part of solved Geometry questions and answers : >> Elementary Mathematics >> Geometry

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