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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.
उत्तर
To Prove: Seg OR bisects ∠MRN as well as ∠MON
Proof: In ΔMRO and ΔNRO
seg OM ≅ seg ON ...[radii of the circle]
seg OR ≅ seg OR ......[Common side]
seg RM ≅ seg RN ......[Tangent Segment theorem]
By S.S.S. Test
∴ ΔMRO ≅ ΔNRO
∴ ∠MOR ≅ ∠NOR
∴ ∠MRO ≅ ∠NRO
∴ seg OR bisects ∠MRN and ∠MON.
संबंधित प्रश्न
In the adjoining figure, O is the centre 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
- What is the length of each tangent segment?
- What is the measure of ∠MRO?
- What is the measure of ∠MRN?
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. 
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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.
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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 –
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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.
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AB = AC ......[`square`] (II)
But OB = OC = r ......[`square`] (III)
From (i), (ii) and (iii)
AB = `square` = OB = OC = r
∴ Quadrilateral ABOC is `square`
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If one angle of `square` is right angle, then it is a square.
∴ Quadrilateral ABOC is a square.
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Use the information and fill in the boxes with proper numbers.
(i) m(arcAXB) =
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Given: In a circle with centre B
arc APC ≅ arc DQE
To Prove: Chord AC ≅ chord DE
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∆ABC ≅ ∆DBE ......`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?
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