Multiple Choice QuestionsIf ABCD be a cyclic quadrilateral in which ∠A = 4x°, ∠B = 7x°, ∠C = 5y°, ∠D = y°, then x : y is
3 : 4
4 : 3
5 : 4
4 : 5
ABCD is a cyclic quadrilateral and AD is a diameter. If ∠DAC = 55° then value of ∠ABC is
55°
35°
145°
145°
All sides of a quadrilateral ABCD touch a circle. If AB = 6 cm, BC = 7.5 cm, CD = 3 cm, then DA is
3.5 cm
4.5 cm
2.5 cm
2.5 cm
D.
2.5 cm
As tangents drawn from external point are equal
∴ AE = AH ...(i)
BE = BF ...(ii)
GC = FC ...(iii)
GD = HD ...(iv)
Adding (i), (ii) (iii), (iv)
⟹ AE + BE + GC + GD = AH + BF + FC + HD
⟹ AB + CD = AD + BC
⟹ 6 + 3 = AD + 7.5
⟹ AD = 9 - 7.5 = 1.5 cm
Inside a square ABCD, ΔBEC is an equilateral triangle. If CE and BD intersect at O. then ∠BOC is equal to
60°
75°
90°
90°
ABCD is a rectangle where the ratio of the lengths of AB and BC is 3 : 2. If P is the mid point of AB, then the value of 
is
If a regular polygon has each of its angles equal to 
times of two right angles, then the number of sides is
3
5
6
6
The sum of all interior angles of a regular polygon is twice the sum of all its exterior angles. The number of sides of the polygon is
10
8
12
12
The ratio between the number of sides of two regular polygons is 1 : 2 and the ratio between their interior angles is 2 : 3. The number of sides of these polygons is respectively.
6, 12
5, 10
4, 8
4, 8
The interior angle of a regular polygon exceeds its exterior angle by 108°. The number of the sides of the polygon is
12
16
14
14
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