Two circles touch each other internally. Their radii are 3 cm and 5 cm. The biggest chord of the greater circle which is outside the inner circle is of length?

2 \(\sqrt 2\) cm
3 \(\sqrt 6\) cm
4 \(\sqrt 6\) cm
6\(\sqrt 2\) cm

LohaHridoy

4 views

2025-01-04 04:42

1 Answers

AhmedNazir

Option 3 : 4 \(\sqrt 6\) cm

Look at the figure, we can easily infer that AB is the largest chord of the bigger circle just outside the smaller circle.

[ alt="20" src="//storage.googleapis.com/tb-img/production/18/03/20.PNG" style="height:217px; width:179px">

Let centers of bigger and smaller circles be ‘O’ and ‘o’ respectively.

In ΔAOE,

AE² + EO² = AO²

⇒ AE² + 1² = 5²

⇒ AE² = 25 - 1

⇒ AE² = 24 = 2² × 6

⇒ AE = 2√6 cm

⇒ Length of the chord AB = 2 × AE = 2 × 2√6 = 4√6 cm

∴ Length of the chord AB = 4√6 cm

4 views Answered 2022-09-04 04:29

Related Questions

PAB is a tangent which is common to two circles which touches each other at point X. The tangent touches the smaller circle at A and larger circle at B. If PA = 20 cm and the radius of smaller circle is 15 cm, then find the radius of larger circle.?

1 Answers 5 Views

If two equal circles of radius 5 cm have two common tangents AB and CD which touch the circles at point A, B, C and D. If CD = 18 cm then find the length of AB.?

1 Answers 7 Views

Two concentric circles with centre O has a common chord AB of length 18 cm which intersects the smaller circle at points C and D. Radius of smaller circle is 6 cm and BP is the tangent to the smaller circle of length 8 cm. Find the length of the chord CD to the smaller circle.?

1 Answers 4 Views

Consider a circle with centre at C. Let OP, OQ denote respectively the tangents to the circle drawn from a point O outside the circle. Let R be a point on OP and S be a point on OQ such that OR × SQ = OS × RP. Which of the following statement(s) is/are correct (1) If X is the circle with centre at O and radius OR, and Y is the circle with centre at O and radius OS, then X = Y (2) ∠POC + ∠QCO = 90° Select the correct answer using the code given below.?

1 Answers 6 Views

Consider a circle with centre at O and radius 7 cm. Let QR be the chord of length 2 cm and let P be the midpoint of QR. Let CD be another chord of this circle passing through P such that ∠CPQ is acute. If M is the midpoint of CD and MP = √24 cm, then which of the following statements are correct (1) ∠QPD = 135° (2) If CP = m cm and PD = n cm, then m and n are the roots of the quadratic equation x2 – 10x + 1 = 0 (3) The ratio of triangle OPR to the area of triangle OMP is 1 ∶ 2√2 Select the correct answer using the code given below.?

1 Answers 7 Views

AB is the chord of circle of length 6 cm. From the center of the circle a perpendicular is drawn which intersects the chord at D and distance between centre and chord is 4 cm. ﬁnd the area (in cm2) of the circle)?

1 Answers 5 Views

Which of the following statements is/are true about the types of gauge in Indian Railways I. In Broad gauge. the clear distance between the inner faces of two rails is 1.676 m II. In Meter gauge. the clear distance between the inner faces of two rails is 1.240 m III. In Narrow gauge. the clear distance between the inner faces of two rails is 0.762 m?

1 Answers 7 Views

In making decisions about important questions, it is desirable to be able to distinguish between strong and weak arguments. Strong arguments are those, which are both important and directly related to the question. Weak arguments are those, which are of minor importance and also may not be directly related to the question or may be related to a trivial aspect of the question. The questions below are followed by two arguments each numbered I and II. You have to decide which of the two arguments is the strong argument and which is the weak argument. Statement: In a competitive market, if one firm reduces its prices then should other firms also reduce their prices Arguments: Yes. If the other firms do not reduce their prices, they would lose customers. No. The other firms will start facing losses by reducing their prices.?

1 Answers 5 Views

The length of a chord of a circle is equal to the radius of the circle. The angle which this chord subtends in the major segment of the circle is equal to:?

1 Answers 5 Views

In the following question the 1st and the last part of the sentence/passage are numbered 1 and 6. The rest of the sentence/ passage is split into four parts and named P, Q, R and S. These four parts are not given in their proper order. Read the sentence/passage and find out which of the four combinations is correct.. 1. Industrially raised chicken can be abnormally forceful, and are regularly kept in obscured sheds to avoid them pecking at each other. P. The feathered creatures invested much a greater amount of their energy—up to a third—pecking at the lifeless things in the pens, as opposed to fowls in different pens which invested a considerable measure of time assaulting others. Q. In low light conditions, they carry on less pugnaciously, yet are more inclined to ophthalmic scatters and respiratory issues. R. In an examination, forceful head-pecking was everything except killed among fowls in the improved condition. S. Modifying the birds’ condition, by adding parcels of wood-shavings to their pens, can work wonders. 6. Bundles could lessen forcefulness and decrease wounds; they may even enhance efficiency, since a glad chicken is a profitable chicken.?

1 Answers 4 Views

এক্সাম দিয়ে মেধা যাচাই করুন

Job Preparation (1125)

Admission (754)

এসএসসি (10)

এইচএসসি (5)