TRIANGLES (CDS)

Total Questions: 69

21. If angle A of triangle ABC is 30° and the circum-radius of the triangle is 10 cm, then what is the length of side BC? [2017 (II) Evening Shift]

Correct Answer: (b) 10 cm
Solution:We have, in ∆ABC,

22. If a triangle ABC, AD is perpendicular on BC. If angle BAC = 90 deg, AB = c, BC = a, CA = b and AD = p then which one of the following correct? [2017 (II) Evening Shift]

Correct Answer: (c) p = (bc)/a
Solution:In ∆ABC, AD is perpendicular on BC

23. In an equilateral triangle ABC, BD is drawn perpendicular to AC. What is BD² equal to? [2017 (II) Evening Shift]

Correct Answer: (c) AD²
Solution:We have, ABC is an equilateral triangle

24. If PL, QM and RN are the altitudes of triangle PQR whose orthocentre is O, then Q is the orthocentre of the triangle. [2017 (II) Evening Shift]

Correct Answer: (d) OPR
Solution:We know that, orthocentre is intersection point of altitude of triangle.

25. In triangle ABC, angle C = 90 deg and CD is the perpendicular from C to AB. If (CD)⁻² = (BC)⁻² + (CA)⁻², then which one of following is correct? [2017 (II) Evening Shift]

Correct Answer: (d) AB ⋅ CD = BC ⋅ CA
Solution:


26. In a triangle ABC, the medians AD and BE intersect at G. A line DF is drawn parallel to BE such that F is on AC. If AC = 9 cm, then what is CF equal to? [2017 (II) Evening Shift]

Correct Answer: (a) 2.25 cm
Solution:In ∆BEC, GE is parallel to DF

27. In a trianlge PQR, X is a point on PR and Y is a point on QR such that PR =10 cm, RX = 4cm, YR = 2 cm, QR = 5 cm. What one of the following is correct? [2017 (II) Evening Shift]

Correct Answer: (a) XY is parallel to PQ
Solution:We have, In ∆PQR, PR = 10 cm, RX = 4 cm, RY = 2 cm QR = 5 cm

28. Consider the following statements [2017 (II) Evening Shift]

1. The point of intersection of the perpendicular bisectors of the sides of a triangle may lie outside the triangle.
2. The point of intersection of the perpendicular drawn from the vertices to the opposite side of a triangle may lie on two sides.

Which of the above statements is/are correct?

Correct Answer: (c) Both 1 and 2
Solution:1. The point of intersection of the perpendicular bisectors of the sides of a triangle is the circumcentre of triangle, Therefore, the circumcentre of obtuse-angle triangle lies outside the circle.
∴Statement 1 is correct.
2. Yes, In case of right angled triangle, the point of intersection of the perpendiculars drawn from the vertices to the opposites sides i.e on the right angle vertex, which lies on two sides.

29. The diagonals of a cyclic quadrilateral ABCD intersect at P and the area of the triangle APB is 24 square cm. If AB = 8 cm and CD = 5 cm, then what is the area of the triangle CPD [2017 (II) Evening Shift]

Correct Answer: (d) 9.375 cm²
Solution:We have ABCD is cyclic quadrilateral AB = 8 cm


30. One-fifth of the area of a triangle ABC is cut off by a line DE drawn parallel to BC such that D is on AB and E is on AC. If BC =10 cm, then what is DE equal to? [2017 (II) Evening Shift]

Correct Answer: (b) 2√5 cm
Solution:Since, DE BC || , therefore ∠ADE = ∠ABC and ∠AED = ∠ACB