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महाराष्ट्र राज्य शिक्षण मंडळएस.एस.सी (इंग्रजी माध्यम) इयत्ता १० वी

In the Following Figure ‘O’ is the Centre of the Circle.∠Aob = 1100, M(Arc Ac) = 450.Use the Information and Fill in the Boxes with Proper Numbers.(I) M(Arcaxb) = - Geometry Mathematics 2

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प्रश्न

In the following figure ‘O’ is the centre of the circle.

∠AOB = 1100, m(arc AC) = 450.

Use the information and fill in the boxes with proper numbers.

(i) m(arcAXB) =

(ii)m(arcCAB) =
(iv)∠COB =

(iv)m(arcAYB) =

उत्तर

From the figure,
(i) m(arc AXB) = 110°
(ii) m(arc CAB) = 155°
(iii) ∠COB = 155°
(iv) m(arc AYB) = 250°

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Tangent Segment Theorem
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
2018-2019 (March) Balbharati Model Question Paper Set 2

संबंधित प्रश्‍न

Seg RM and seg RN are tangent segments of a circle with centre O. Prove that seg OR bisects ∠MRN as well as ∠MON with the help of activity.


In the given figure, the circles with centres A and B touch each other at E. Line l is a common tangent which touches the circles at C and D respectively. Find the length of seg CD if the radii of the circles are 4 cm, 6 cm. 


Four alternative answers for the following question is given. Choose the correct alternative.
 Length of a tangent segment drawn from a point which is at a distance 12.5 cm from the centre of a circle is 12 cm, find the diameter of the circle.


Four alternative answers for the following question is given. Choose the correct alternative.

 Seg XZ is a diameter of a circle. Point Y lies in its interior. How many of the following statements are true ? (i) It is not possible that ∠XYZ is an acute angle. (ii) ∠XYZ can’t be a right angle. (iii) ∠XYZ is an obtuse angle. (iv) Can’t make a definite statement for measure of ∠XYZ.


In the given figure, M is the centre of the circle and seg KL is a tangent segment.
If MK = 12, KL = \[6\sqrt{3}\] then find –
(1) Radius of the circle.
(2) Measures of ∠K and ∠M.


In the given figure, O is the centre of the circle. Seg AB, seg AC are tangent segments. Radius of the circle is r and l(AB) = r, Prove that ▢ABOC is a square. 

Proof: Draw segment OB and OC.

l(AB) = r      ......[Given] (I)

AB = AC    ......[`square`] (II)

But OB = OC = r    ......[`square`] (III)

From (i), (ii) and (iii)

AB = `square` = OB = OC = r

∴ Quadrilateral ABOC is `square`

Similarly, ∠OBA = `square`      ......[Tangent Theorem]

If one angle of `square` is right angle, then it is a square.

∴ Quadrilateral ABOC is a square.


The perpendicular height of a cone is 12 cm and its slant height is 13 cm. Find the radius of the base of the cone. 


In the given figure, M is the centre of the circle and seg KL is a tangent segment. L is a point of contact. If MK = 12, KL = `6sqrt3`, then find the radius of the circle.


Prove the following theorem:

Tangent segments drawn from an external point to the circle are congruent.


Segment DP and segment DQ are tangent segments to the circle with center A. If DP = 7 cm. So find the length of the segment DQ.


Length of a tangent segment drawn from a point which is at a distance 15 cm from the centre of a circle is 12 cm, find the diameter of the circle?


Tangent segments drawn from an external point to a circle are congruent, prove this theorem. Complete the following activity.


Given: `square`

To Prove: `square`

Proof: Draw radius AP and radius AQ and complete the following proof of the theorem.

In ∆PAD and ∆QAD,

seg PA ≅ `square`      .....[Radii of the same circle]

seg AD ≅ seg AD    ......[`square`]

∠APD ≅ ∠AQD = 90°     .....[Tangent theorem]

∴ ∆PAD ≅ ∆QAD    ....[`square`]

∴ seg DP ≅ seg DQ  .....[`square`]


In the adjoining figure, O is the center of the circle. From point R, seg RM and seg RN are tangent segments touching the circle at M and N. If (OR) = 10 cm and radius of the circle = 5 cm, then

(i) What is the length of each tangent segment?

(ii) What is the measure of ∠MRO?

(iii) What is the measure of ∠MRN?


If AB and CD are the common tangents in the circles of two unequal (different) radii, then show that seg AB ≅ seg CD.


Seg RM and seg RN are tangent segments of a circle with centre O. Prove that seg OR bisects ∠MRN as well as ∠MON with the help of activity.


Proof: In ∆RMO and ∆RNO,

∠RMO ≅ ∠RNO = 90°   ......[`square`]

hypt OR ≅ hypt OR    ......[`square`]

seg OM ≅ seg `square`    ......[Radii of the same circle]

∴ ∆RMO ≅ ∆RNO      ......[`square`]

∠MOR ≅ ∠NOR

Similairy ∠MRO ≅ `square`    ......[`square`]


Prove that, tangent segments drawn from an external point to the circle are congruent.


In a parallelogram ABCD, ∠B = 105°. Determine the measure of ∠A and ∠D.


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