Q1. ABCD is a rhombus in which, side AB = 4 cm and ∠ABC=120°, then the length of the diagonal BD is
(a) 1 cm
(b) 6 cm
(c) 3 cm
(d) 4 cm
Q2. A line drawn parallel to BC in ∆ABC intersects its side AB and AC at point D and E respectively. If area of ∆ ABE is 36 cm2 then the area of ∆ACD is
(a) 18 cm2
(b) 36 cm2
(c) 28 cm2
(d) 39 cm2
Q3. If the radius of the circumcircle of an equilateral triangle is 10 cm, then what will be the radius of the incircle inscribed in it?
(a) 5 cm
(b) 10 cm
(c) 20 cm
(d) 15 cm
Q4. Point O is the centroid of ∆ABC and AD, BE and CF are its medians. If area of ∆AOE=15 cm^2, then the area of quadrilateral BDOF is
(a) 20 cm2
(b) 30 cm2
(c) 40 cm2
(d) 25 cm2
Q5. The radii of two concentric circles are 9 cm and 15 cm. If a chord of the bigger circle is tangent on the smaller circle, then the length of that chord is
(a) 24 cm
(b) 12 cm
(c) 30 cm
(d) 18 cm
Q6. The length of a chord of a circle is equal to its radius. The value of the angle subtended by this chord at the centre of the circle is
(a) 30°
(b) 45°
(c) 60°
(d) 90°
Q7. In ∆ABC, AD is the internal bisector of ∠A and it meets with side BC at point D. If BD = 5 cm, BC = 7.5 cm, then AB : AC is
(a) 2 : 1
(b) 1 : 2
(c) 4 : 5
(d) 3 : 5
Q8. Point O is the incentre of ∆ABC and ∠A = 30°. Then value of ∠BOC is
(a) 100°
(b) 105°
(c) 110°
(d) 90°
Q9. The two chords AB and AC are 8 cm and 6 cm long respectively. If ∠BAC = 90°, then radius of the circle is
(a) 25 cm
(b) 20 cm
(c) 4 cm
(d) 5 cm
Q10. Which one of the following values can never be the measure of an internal angle of a regular polygon?
(a) 150°
(b) 105°
(c) 108°
(d) 144°
Solutions
S1. Ans.(d)
Sol.
∠ABC = 120°
∴ ∠ABD = 60°
∠ABD = ∠ADB = 60°
∵ AB = AD
∴ ∆ABD is an equilateral ∆.
∴ BD = 4 cm
S3. Ans.(a)
Sol. Since the ratio of the radius of incircle and circumcircle of an equilateral ∆ is 1 : 2.
∴ Radius of the incircle =10/2=5 cm
S10. Ans.(b)
Sol.
By taking ((n-2) × 180°)/ n = 105°
5n = 24°
n = 24/5, which is not possible.
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