In circle, given below, O is its centre and lengths of chords AB and CD are in the ratio 5 : 3 . If ∠ AOB = 100 ° , find the ratio between the arc AB ⏜ and arc CD ⏜

OA = OB = OC = OD = Radius = R ⇒ AB 2 = OA 2 + OB 2 - 2 OA . OB cos ∠ AOB ⇒ AB 2 = OA 2 + OB 2 - 2 OA . OB cos ∠ AOB ⇒ AB 2 = R 2 + R 2 - 2 R 2 cos 100 ° ⇒ AB 2 = R 2 - 2 R 2 cos 100 ° ⇒ AB 2 = 2 R 2 ( 1 - cos 100 ° ) ⇒ AB 2 = 2 R 2 2 sin 2 50 ° ⇒ AB = 2 R sin 50 ° ⇒ AB 2 = R 2 + R 2 - 2 R 2 cos 100 ° ⇒ AB 2 = R 2 - 2 R 2 cos 100 ° ⇒ AB 2 = 2 R 2 ( 1 - cos 100 ° ) ⇒ AB 2 = 2 R 2 2 sin 2 50 ° ⇒ AB = 2 R sin 50 ° Similarly, CD = 2 R sin ∠ COD 2 Given, A B : C D = 5 : 3 ⇒ 5 3 = 2 Rsin 50 ° 2 R sin ∠ COD 2 ⇒ sin ∠ COD 2 = 3 5 sin 50 ° ⇒ sin ∠ COD 2 = 3 5 × 0 . 766 ⇒ sin ∠ COD 2 = 0 . 4596 ⇒ ∠ COD 2 = 27 . 36 ° ∴ ∠ COD = 54 . 72 ° A B ⏜ C D ⏜ = 100 π 180 R 54 . 73 π 180 R = 1 . 83 = 183 100 Hence, the ratio of the arcs is 183 : 100

E M B I B E

Concise Mathematics I.C.S.E - Class IX>Chapter 31 - Chapterwise Revision-(Stage 3)>CHAPTERWISE REVISION>Q 89

MEDIUM

9th ICSE

IMPORTANT

Earn 100

If two arcs of a circle are congruent, then their corresponding chords are equal. Prove it.

Important Questions on Chapterwise Revision-(Stage 3)

HARD

9th ICSE

IMPORTANT

Concise Mathematics I.C.S.E - Class IX>Chapter 31 - Chapterwise Revision-(Stage 3)>CHAPTERWISE REVISION>Q 90

In a circle of radius

5 cm, PQ and RS

are two parallel chords of lengths

8 cm and 6 cm

respectively. Calculate the distance between the chords if they are on the same side of the centre.

HARD

9th ICSE

IMPORTANT

Concise Mathematics I.C.S.E - Class IX>Chapter 31 - Chapterwise Revision-(Stage 3)>CHAPTERWISE REVISION>Q 90

In a circle of radius

5 cm, PQ and RS

are two parallel chords of lengths

8 cm and 6 cm

respectively. Calculate the distance between the chords if they are on the opposite sides of the centre.

HARD

9th ICSE

IMPORTANT

Concise Mathematics I.C.S.E - Class IX>Chapter 31 - Chapterwise Revision-(Stage 3)>CHAPTERWISE REVISION>Q 91

AB and CD

are two chords such that,

AB = 10 cm, CD = 24 cm and AB ∥ CD

. The distance between the chords is

17 cm

. Find the radius of the circle.

HARD

9th ICSE

IMPORTANT

Concise Mathematics I.C.S.E - Class IX>Chapter 31 - Chapterwise Revision-(Stage 3)>CHAPTERWISE REVISION>Q 92

In circle, given below, $O$ is its centre and lengths of chords $AB and CD$ are in the ratio $5 : 3 .$

Question Image

If $∠ AOB = 100 °$ , find $∠ COD$ .

HARD

9th ICSE

IMPORTANT

Concise Mathematics I.C.S.E - Class IX>Chapter 31 - Chapterwise Revision-(Stage 3)>CHAPTERWISE REVISION>Q 92

In circle, given below, $O$ is its centre and lengths of chords $AB and CD$ are in the ratio $5 : 3 .$

Question Image

If $∠ AOB = 100 °$ , find the ratio between the $arc \overset{⏜}{AB} and arc \overset{⏜}{CD}$

HARD

9th ICSE

IMPORTANT

Concise Mathematics I.C.S.E - Class IX>Chapter 31 - Chapterwise Revision-(Stage 3)>CHAPTERWISE REVISION>Q 93

A chord

CD

of a circle, with centre

O

, is bisected by the diameter

AB

at a point

P

. If

OA = OB = 30 cm

and

OP = 18 cm,

calculate

CD

.

HARD

9th ICSE

IMPORTANT

Concise Mathematics I.C.S.E - Class IX>Chapter 31 - Chapterwise Revision-(Stage 3)>CHAPTERWISE REVISION>Q 93

A chord

CD

of a circle, with centre

O

, is bisected by the diameter

AB

at a point

P

. If

OA = OB = 30 cm

and

OP = 18 cm,

calculate

AD

.

HARD

9th ICSE

IMPORTANT

Concise Mathematics I.C.S.E - Class IX>Chapter 31 - Chapterwise Revision-(Stage 3)>CHAPTERWISE REVISION>Q 94

If two equal chords of a circle intersects each other within the circle, prove that the segments of one chord are equal to the corresponding segments of other chords.

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