ΔABC is isosceles having AB = AC and ∠A = 40°. Bisectors PO

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 Multiple Choice QuestionsMultiple Choice Questions

21.

The midpoints of AB and AC of triangle ABC are X and Y respectively. If BC + XY = 12 units, then BC - XY  is

  • 10 units

  • 8 units

  • 6 units

  • 6 units

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22.

In an isosceles increment ABC comma space AD is the median to the unequal side meeting BC at D. DP is the angle bisector of angle ADB and PQ is drawn parallel to BC meeting AC at Q. Then the measure of angle PDQ is

  • 130 degree
  • 90 degree
  • 180 degree
  • 180 degree
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23.

If in △ ABC, DE ∥ BC, AB = 7.5 cm, BD = 6 cm and DE = 2 cm then the length of BC in cm is

  • 6

  • 8

  • 10

  • 10

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24.

Suppose that the medians BD, CE and AF of a triangle ABC meet at G. Then AG : GF is

  • 1: 2

  • 2 : 1

  • 1 : 3

  • 1 : 3

232 Views

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25.

In ΔABC, AC = BC and ∠ABC = 50°, the side BC is produced to D so that BC = CD then the value of ∠BAD is

  • 80°

  • 40°

  • 90°

  • 90°

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26.

ΔABC is isosceles having AB = AC and ∠A = 40°. Bisectors PO and OQ of the exterior angles ∠ABD and ∠ACE formed by producing BC on both sides, meet at O. Then the value of ∠BOC is

  • 70°

  • 110°

  • 80°

  • 80°


A.

70°


AB  = AC

therefore space space angle ABC space equals space angle ACB space equals space 140 over 2 space equals space 70 degree
therefore space space angle ABD space equals space angle ACE space equals space 180 degree space minus space 70 degree space equals space 110 degree

therefore space space angle PBD equals space 55 degree space equals space angle CBO
angle QCE space equals space angle BCO space equals space 55 degree
therefore space space space angle BOC space equals space 180 degree space minus space 2 space cross times space 55 degree
space space equals space 180 degree space minus space 110 degree space equals space 70 degree
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27.

ΔABC is a triangle, PQ is line segment intersecting AB in P and AC in Q and PQ || BC. The ratio of AP : BP = 3 : 5 and length of PQ is 18 cm. The length of BC is

  • 28 cm

  • 48 cm

  • 84 cm

  • 84 cm

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28.

If the sides of a triangle are in the ratio 3 space colon thin space 1 1 fourth space colon space 3 1 fourth then the triangle is 

  • Right triangle

  • Obtuse triangle

  • Equiangular triangle

  • Equiangular triangle

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29.

In a right angled triangle ΔPQR, PR is the hypotenuse of length 20 cm, angle PRQ space equals space 30 degree comma the area of the triangle is

  • 50 square root of 3 space cm squared
  • 100 square root of 3 space cm squared
  • 25 square root of 3 space cm squared
  • 25 square root of 3 space cm squared
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30.

ABC is a triangle in which DE || BC and AD : DB = 5 : 4. Then DE : BC is

  • 4 : 5

  • 4 : 9

  • 9 : 5

  • 9 : 5

357 Views

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