ADVANCED MATHS QUIZ: GEOMETRY

1. The perimeter of a rhombus is 146 cm and one of its diagonals is 55 cm. The other diagonal is 

(1) 92 cm

(2) 73 cm

(3) 48 cm

(4) 72 cm

2. In a right-angled triangle ABC, ∠ABC=90°, AB=5 cm and BC=12 cm. The radius of the circumcircle of the triangle ABC is

(1) 7.5 cm

(2) 6 cm

(3) 6.5 cm

(4) 7 cm

3. Two circles intersect at A and B. P is a point on produced BA. PT and PQ are tangents to the circles. The relation of PT and PQ is

(1) PT=2PQ

(2) PT<PQ

(3) PT>PQ

(4) PT=PQ

4. If O is the circumcentre of ∆ABC and OD⊥BC,  then ∠BOD must be equal to 

(1) ∠A

(2) 1/2∠A

(3) 1/2∠B 

(4) 1/2∠C

5. A, B and C are the three points on a circle such that the angles subtended by the chords AB and AC at the centre O are 90° and 110° respectively ∠BAC   is equal to

(1) 70°

(2) 80°

(3) 90°

(4) 100°

6. ABC is a triangle. The internal bisector of the angles ∠A,∠B and ∠C intersect the circumcircle at X, Y and Z respectively. If ∠A=50°,∠CZY=30°, then ∠BYZ, then  will be

(1) 45°

(2) 55°

(3) 35°

(4) 30°

7. If a circle with radius of 10 cm has two parallel chords 16 cm and 12 cm and they are on the same side of the centre of the circle, then the distance between the two parallel chords is

(1) 2 cm

(2) 3 cm

(3) 5 cm

(4) 8 cm

8. Two circles of radii 8 cm and 2 cm respectively touch each other externally at the point A. PQ is the direct common tangent of those two circles of centres O₁ and O₂ respectively. Then length of PQ is equal to

(1) 2 cm

(2) 3 cm

(3) 4 cm

(4) 8 cm

9. Two circles touch each other externally at a point P and a direct common tangent touches the circles at the points Q and R respectively. Then ∠QPR is 

(1) 45°

(2) 180°

(3) 90°

(4) 60°

10. ABCD is a cyclic quadrilateral whose vertices are equidistant from the point O (centre of the circle). If ∠COD=120° and ∠BAC=30°, then the measure of ∠BCD is 

(1) 180°

(2) 150°

(3) 60°

(4) 90°

Solutions: