Plane Geometry
- The sides AB and AC of ΔABC have been produced to D and E respectively. The bisectors of ∠CBD and ∠BCE meet at O. If ∠A = 40°, then ∠BOC is equal to:
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As we know the formula,
∠BOC = 90° - 1 ∠A 2 Correct Option: D
As we know the formula,
∠BOC = 90° - 1 ∠A 2 ∴∠BOC = 90° - 1 (40°) 2
= 90° - 20°
∠BOC = 70°
- In the given figure, DE || BC if AD = 1.7 cm, AB = 6.8 cm and AC = 9 cm, find AE.
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Since DE || BC, We can use the formula,
∴ AB = AC AD AE
Correct Option: A
Since DE || BC,
∴ AB = AC AD AE ∴ 68 = 9 17 AE or , AE = 9 = 2.25cm 4
- If the bisector of an angle of Δ bisects the opposite side, then the Δ is :
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According to given question, ∠1 = ∠2
∴ AB = BD AC AD
Correct Option: B
Since ∠1 = ∠2
∴ AB = BD AC AD
But BD = CD (given)∴ AB = 1 AC
AB = AC
∴ the given ∆ is isosceles
- The areas of two similar Δs are 81 cm2 and 144 cm2. If the largest side of the smaller Δ is 27 cm, then the largest side of the larger Δ is :
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Let ABC and DEF be the two similar Δs having area 81 cm2 and 144 cm2 respectively:
Let BC = 27 cm
Then since ΔABC ∼ ΔDEF∴ area (∆ABC) = BC2 (area Theorem) area (∆DEF) EF2 Correct Option: C
Let ABC and DEF be the two similar Δs having area 81 cm2 and 144 cm2 respectively:
Let BC = 27 cm
Then since ΔABC ∼ ΔDEF∴ ar (∆ABC) = BC2 (area Theorem) ar(∆DEF) EF2 81 = (27)2 ⇒ 9 = 27 144 x2 12 x
∴ x = 36 cm.
- In the given figure ∠BAD = ∠CAD. AB = 4 cm, AC = 5.2 cm, BD = 3 cm. Find BC.
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According to question, Given that
∠BAD = ∠CAD. AB = 4 cm, AC = 5.2 cm, BD = 3 cm
In ΔABC, AD is the bisector of ∠AAB = BD (Internal bisector prop.) AC CD Correct Option: A
According to question, Given that
∠BAD = ∠CAD. AB = 4 cm, AC = 5.2 cm, BD = 3 cm
In ΔABC, AD is the bisector of ∠AAB = BD (Internal bisector prop.) AC CD 4 = 3 ⇒ DC = 3.9 cm 5.2 DC
But BC = BD + CD = 3cm + 3.9 cm = 6.9 cm