The length of the tangent drawn from a point 13 cm away from the centre of a circle of radius 5 cm is
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Answer: Option C — 12 cm
Detailed Solution
The radius is perpendicular to the tangent at the point of contact, so the triangle is right-angled.
Tangent cm.
✓ Check
5, 12, 13 is a Pythagorean triple.⚠ Common trap
(A) 8 cm — subtracts the lengths: 13 − 5.Quick tip
Tangent length
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Geometry — Preparation
This question tests your understanding of Geometry, a key topic in the Quantitative Aptitude section. The detailed solution above uses a step-by-step approach to show the reasoning, and where available, a shortcut that helps you solve similar questions in under 90 seconds during the actual exam.
Geometry in entrance exams covers lines and angles, triangles, quadrilaterals, polygons and circles. Questions test properties of angles formed by parallel lines, congruence and similarity of triangles, the Pythagorean theorem, properties of special quadrilaterals, interior and exterior angles of polygons, and circle theorems such as angles in the same segment and tangent properties. Most geometry questions are solved by recognising the right property, not by long calculation. A neat rough diagram, labelled with the given information, often reveals the answer. Pythagorean triplets (3-4-5, 5-12-13, 8-15-17) and the 30-60-90 and 45-45-90 triangle ratios are worth memorising because they appear repeatedly. Practise the geometry questions below. Each comes with a step-by-step solution that names the property used.