ABDC is a parallelogram in which diagonals AD and BC intersect at O. AE and DF are perpendiculars on BC at E and F, respectively. Which of the following is NOT true?
A. ΔABC ≅ ΔDCB
B. ΔAOE ≅ ΔDOF
C. ΔAEB ≅ ΔDFC
D. ΔADC ≅ ΔABD
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In the given figure, chords AD and BC in the circle, are extended to E and F, respectively.
If ∠CDE = 85°, ∠DCF = 94°, then the value of ∠ABF + ∠EAB is:
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If one side of a triangle is 7 with its perimeter equal to 18, and area equal to
108 , then the other two sides are:
A. 6 and 5
B. 3.5 and 7.5
C. 7 and 4
D. 3 and 8
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In a circle, a diameter AB and a chord PQ (which is not a diameter) intersect each other X perpendicularly. If AX : BX = 3 : 2 and the radius of the circle is 5 cm, then the length of chord PQ is
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ABCD is a cyclic quadrilateral Diagonals BD and AC intersect each other at E. If ∠BEC = 128° and ∠ECD = 25°, then, what is the measure of ∠BAC?
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The perimeter of a triangle with sides of integer values is equal to 13. How many such triangles are possible?
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ABCDE is a regular pentagon. Its sides are extended as shown in the figure. The value of
6 ∠ ABC + 2∠ EGD + 3∠ BAJ = ?
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Two parallel chords are drawn in a circle of diameter 20 cm. The length of one chord is 16 cm and the distance between the two chords is 12 cm. The length of the other chord is:
A. 20 cm
B. 18 cm
C. 16 cm
D. 12 cm
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In a ΔXYZ, XO is the median and XO = 2 1 YZ. If ∠YXO = 30°, then what is the value of ∠XYZ?
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ln ΔPQR, O is the incentre and ∠P = 42°. Then what is measure of ∠QOR?
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ABCD is a square and ΔMAB is an equilateral triangle. MC and MD are joined. What is the degree measure of ∠MDC?
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Two chords of length a unit and b unit of a circle make angles 60° and 90° at the centre of a circle respectively, then the correct relation is:
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In a triangle ABC, P and Q are point on AB and AC, respectively, such that AP = 1 cm, PB = 3 cm, AQ = 1.5 cm and CQ = 4.5 cm. If the area off ΔAPQ is 12 cm
2 , then find the area of BPQC.
A. 192 cm2
B. 182 cm2
C. 190 cm2
D. 180 cm2
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If in the given figure, ∠ACB + ∠BAC = 80°, ∠BDE = 35°, ∠BCE = 45°, then the marked angle ∠CED is:
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ABC is a cyclic triangle and the bisectors of ∠BAC, ∠ABC and ∠BCA meet the circle at P, Q and R respectively. Then the angle ∠RQP is:
A. 9 0 ∘ − 2 B
B. 9 0 ∘ + 2 C
C. 9 0 ∘ − 2 A
D. 9 0 ∘ + 2 B
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In the given figure, AB, AC and EF are tangents to a circle. If AC = 15 and DE = 3 cm. Then the length of AE is:
A. 24 cm
B. 9 cm
C. 18 cm
D. 12 cm
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In a ΔABC, ∠BAC = 90° and AD is perpendicular to BC where D is a point on BC. If BD = 4 cm and CD = 5 cm, then the length of AD is equal to:
A. 6 cm
B. 4.5 cm
C. 2√5 cm
D. 5√2 cm
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Length of the sides of a triangle are a, b and c respectively. If a2 + b2 + c2 = ab + bc + ca then the triangle is
A. isosceles
B. equilateral
C. scalene
D. right-angled
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In a trapezium ABCD, DC || AB, AB = 12 cm and DC = 7.2 cm. What is the length of the line segment joining the midpoints of its diagonals?
A. 3.6 cm
B. 2.6 cm
C. 4.8 cm
D. 2.4 cm
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A triangle with the lengths of its sides proportional to the numbers 7, 24 and 30 is:
A. acute angled
B. obtuse angled
C. not possible
D. right angled
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