Triangles and Circles (Class 10)

What this worksheet covers

This is an eighteen-question practice worksheet on triangles and circles for Class 10, written to the pattern of the SOF International Mathematics Olympiad (IMO). It carries 24 marks and is designed to be attempted in 45 minutes, split across three sections — Mathematical Reasoning, Everyday Mathematics and Reasoning and Achievers Section. Every question is multiple choice with exactly one correct option, and every one comes with a fully worked solution rather than just an answer key — so a child who gets one wrong can see where the reasoning went astray instead of only learning that it did.

Skills your child practises

• Applied problem-solving on triangles and circles at Class 10 level
• Working accurately against a time limit, as the real paper demands
• Mathematical Reasoning questions in the olympiad format
• Everyday Mathematics and Reasoning questions in the olympiad format
• Achievers Section questions in the olympiad format
• Reading worked solutions to find the step that went wrong

How to use it

1. 1There are 18 questions in this worksheet. All questions are compulsory.
2. 2Each question has four options (A), (B), (C) and (D). Exactly one option is correct.
3. 3Questions 1–15 carry 1 mark each. Questions 16–18 (Achievers Section) carry 3 marks each.
4. 4There is no negative marking. Use of a calculator is not allowed.
5. 5Figures are not drawn to scale unless stated. Rough work may be done at the side of each page.

Sample questions from this worksheet

A preview of what's inside Triangles and Circles (Class 10) — the PDF has the full set, and every question comes with a worked solution like these.

1. 1. Two triangles are similar if their corresponding angles are equal and their corresponding sides are _______.

   • AIn the same ratiocorrect
   • BEqual
   • CPerpendicular
   • DParallel
   Solution: Similar figures have the same shape but not necessarily the same size, so corresponding sides are in the same ratio. Equal corresponding sides would make the triangles congruent, a special case of similarity.

2. 2. The areas of two similar triangles are in the ratio 9 : 16. The ratio of their corresponding sides is _______.

   • A9 : 16
   • B4 : 3
   • C81 : 256
   • D3 : 4correct
   Solution: Since the area ratio is the square of the side ratio, the sides are in the ratio √9 : √16 = 3 : 4.

3. 3. Two tangents PA and PB are drawn from an external point P to a circle with centre O, and the angle between them is 80°. The measure of ∠AOB is _______.

   • A100°correct
   • B90°
   • C80°
   • D160°
   Solution: OAPB is a quadrilateral whose angles at A and B are each 90°, since a radius meets a tangent at right angles. The four angles add to 360°, so ∠AOB = 360° − 90° − 90° − 80° = 100°. The angle at the centre and the angle between the tangents are always supplementary.