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e Bisectors of ∠B and ∠C intersect at O. Prove that m∠BOC = 90 + A2.
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e In the figure, AM¯ is the angle bisector of ∠PAQ, then find PM : MQ.
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| e The point of intersection of the altitudes of a triangle is known as e |
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e The point of intersection of the perpendicular bisectors of a triangle is known as
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| e The point of concurrency of the interior angle bisectors of a triangle is known as e |
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e Find the m∠ADB in the given ΔABC, if AD¯ is the angle bisector of ∠BAC and if m∠ABC = 75 and m∠BCA = 65.
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| e AD¯ is the perpendicular bisector of BC¯. If AD = 24 cm and BD = 7 cm, then find AC. e |
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e If in a triangle ABC, the bisectors of ∠ABC and ∠ACB meet at M, then find m∠BMC when m∠ABC = m∠ACB = 70.
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e Which of the following always lies inside a triangle?
1. incenter
2. orthocenter
3. circumcenter
4. centroid e |
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| e In ΔABC, the bisector AX¯ of ∠A intersects BC¯ at X; XL¯ ⊥ AB¯ and XM¯ ⊥ AC¯. If XL = 10 cm, then what is the length of XM? e |
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| e In which triangle the incenter and circumcenter coincide? e |
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e Bisectors of ∠B and ∠C intersect at O. Prove that m∠BOC = 90 + A2.
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e AD¯ is the angle bisector of ∠CAB. If AC = AB, then find ∠ADB.
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e In the figure, AM¯ is the angle bisector of ∠PAQ, then find PM : MQ.
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e OB¯ and OC¯ are the external bisectors of ∠B and ∠C of ΔABC. If ∠B = x and ∠C = y, then find m∠BOC.
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e In ΔABC, OB¯ and OC¯ are the angle bisectors of ∠B and ∠C respectively. If m∠A = 100 and m∠B = 30, then find m∠BOC.
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e In ΔABC, D is a point on BC¯, m∠ABD = 86, m∠ACD = 44 and AD¯ is the bisector of ∠BAC. What is m∠ADC?
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e In the figure, AE¯ is the angle bisector of ∠A. If m∠B = 30 and m∠C = 40, then find m∠EAD.
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e If the bisectors of ∠B and ∠C of an equilateral triangle meet at O, then what is the measure of ∠BOC?
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| e Two angles of a triangle have the measures as 45º and 65º. Which cannot be the measure of the bisected angle of an exterior angle of the triangle? e |
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e AP¯ bisects ∠A. m∠B = x, m∠ACD = y. Find m∠APC.
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| e The angle bisectors and perpendicular bisectors coincide for a/an e |
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