AP EAPCET (Engineering) Properties of Triangles — practice questions
81 free MCQs with worked solutions. Tap any question for the answer + explanation, or practice them all in the app.
Practice AP EAPCET (Engineering) Properties of Triangles in the app →A triangle has side a = 10 and opposite angle A = 30°. What is its circumradius?In triangle ABC, A = 30°, B = 90° and a = 6. What is the length of side b?Two sides of a triangle are 5 and 8, and the angle between them is 60°. Find the third side.The sides of a triangle are 3, 5 and 7. What is the largest angle?Find the area of a triangle with sides 13, 14 and 15 using Heron's formula.What is the inradius of a triangle with sides 13, 14 and 15?A right triangle has legs 3 and 4 and hypotenuse 5. What is its inradius?If the angles of a triangle are in the ratio 1 : 2 : 3, the sides are in the ratioGiven A = 30°, a = 7 and b = 10, how many triangles can be formed?Which given data can make the sine rule ambiguous?What does the law of cosines reduce to when the angle between two sides is 90°?A triangle has sides 4, 5 and 7. Is it acute, right or obtuse?Sides of 5, 7 and 8 form a triangle. What is the angle opposite the side of length 7?Sides 3 and 5 enclose an angle of 120°. What is the length of the third side?A triangle has two sides of 6 and 10 enclosing 150°. What is its area?A triangle has perimeter 36 and inradius 3. What is its area?A triangle of area 84 has inradius 4. What is its perimeter?The incenter of a triangle is the meeting point of itsThe excenter opposite A lies on the internal bisector of A and theHow many excircles does every triangle have?An excircle of a triangle is tangent to one side and toWhich excircle of a triangle is the largest?How does the incircle radius compare with each exradius of the same triangle?A 6, 8, 10 right triangle has area 24. What is the exradius opposite the side 10?In a triangle with sides 7, 8 and 9, how far is vertex A (opposite 7) from the incircle touchpoints?The two tangent segments drawn from one vertex to the incircle areEuler's theorem gives d² = R(R − 2r). If R = 8 and r = 3, what is the distance d between incenter and circumceFor an equilateral triangle, what is R : r, the circumradius to inradius ratio?The inradius of a triangle is never greater than which fraction of the sum of its altitudes?A line that halves both a triangle's area and its perimeter passes through theA circle touching all three sides of a triangle from inside is called theWhich circle touches the incircle internally and the three excircles externally?In what year did Karl Feuerbach discover his theorem on the nine-point circle?In a tangential quadrilateral, the opposite sidesA polygon of any number of sides that has an inscribed circle is calledThe sides of an excentral triangle lie on which lines of the reference triangle?The nine-point circle passes through side midpoints, altitude feet andIn the sine rule a/sin A = b/sin B = c/sin C, the common value equalsIf R = 4 and sin A = 3/4, what is the side a?The sine rule can find the remaining sides of a triangle when two angles and one side are known. This techniquIn the proof of the sine rule, equating altitudes b sin γ and c sin β givesThe spherical law of sines states that sin A / sin a equalsOn a unit sphere, the sides of a spherical triangle are measured asThe sides of a spherical triangle are arcs of which curves?Another name for the law of cosines in France isIn which Euclid proposition is the obtuse-angle form of the cosine law stated?Who first wrote the law of cosines using algebraic notation, in the 16th century?In the cosine rule, a² − 2ab cos γ + b² − c² = 0 is a quadratic in a. How many positive roots can it have?The law of cosines relates the three sides of a triangle to the cosine ofBy the cosine rule, cos γ in terms of the sides isIf c² > a² + b² in a triangle, the angle γ opposite c isWhich statement about solving triangles with the law of cosines is accurate?Which Persian mathematician computed the most accurate trigonometric tables of his era?The sine of an angle times 2R equals the opposite side. For a triangle with R = 6 and A = 150°, find a.A triangle has sides 3, 4 and 5 and area 6. Using 2R = abc/(2·area), what is R?A triangle has sides 5, 12 and 13. Find its inradius.In triangle ABC, a = 10, A = 30 degrees and B = 45 degrees. Find side b.For a triangle with sides 2, 3 and 4, what is the cosine of its largest angle?What does the law of cosines become when the included angle is a right angle?Using Heron's formula, find the area of a triangle with sides 13, 14 and 15.A right triangle has sides 5, 12 and 13. What is the radius of its incircle?An equilateral triangle has side 6 cm. What is its circumradius?An excenter is found as the intersection of which pair of bisectors?Heron's formula is named after a mathematician from which city?What area does Heron's formula give for sides 3, 4 and 7?Given two angles and one side of a triangle, which rule is the natural way to find the other sides?In a triangle, sin A : sin B : sin C = 3 : 4 : 5. What kind of triangle is it?A triangle has sides 4, 5 and 7. Which statement about it is correct?Which circle is the largest one that fits inside a triangle?Why is Heron's formula unstable for a very small angle?A triangle has sides 5 and 8 enclosing an angle of 60 degrees. What is the third side?In triangle ABC, A = 30 degrees, b = 10 and a = 4. How many such triangles exist?When two sides and a non-included angle are given, the triangle may not be unique. What is this called?The excentral triangle has its sides on which lines?Euclid's Proposition II.12 concerns the square on the side opposite which kind of angle?The law of tangents is mathematically equivalent to which other triangle law?Two sides a, b and the angle between them are known. Which rule gives the difference of the other two angles?Why is the law of cosines safer for finding an angle?Why can a triangle not be fixed when only its three angles are given?When all three sides are given, which rule finds the angles directly?Which fact is true of every triangle?