An isosceles triangle ABC is right-angled at B. D is a point inside the triangle ABC. P and Q are the feet of the perpendiculars drawn from D on the side AB and AC respectively of ΔABC. If AP = a cm, AQ = b cm and ∠BAD = 15°, sin 75° = ?
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In a triangle ABC, the side BC is extended up to D such that CD = AC. If ∠BAD = 109° and ∠ACB = 72° then the value of ∠ABC is
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The equidistant point from the vertices of a triangle is called its:
A. Centroid
B. Incenter
C. Circumcenter
D. Orthocenter
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Let ABC be an equilateral triangle and AX, BY, CZ be the altitudes. Then the right statement out of the four given responses is
A. AX = BY = CZ
B. AX ≠ BY = CZ
C. AX = BY ≠ CZ
D. AX ≠ BY ≠ CZ
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ABC is an isosceles triangle with AB = AC. The side BA is produced to D such that AB = AD. If ∠ABC = 30°, then ∠BCD is equal to
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The sum of three altitudes of a triangle is
A. Equal to the sum of three sides
B. Less than the sum of sides
C. Greater than the sum of sides
D. Twice the sum of sides
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In ΔABC, ∠B = 60° and ∠C = 40°. If AD and AE be respectively the internal bisector of ∠A and perpendicular on BC, then the measure of ∠DAE is
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In a right-angled triangle, the product of two sides is equal to half of the square of the third side i.e., hypotenuse. One of the acute angle must be
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In a ΔABC ∠A : ∠B : ∠C = 2 : 3 : 4. A line CD drawn || to AB, then the ∠ACD is :
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BL and CM are medians of ΔABC right-angled at A and BC = 5 cm. If BL =
2 3 5 cm, then the length of CM is
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In a triangle ABC, ∠A = 90°, ∠C = 55°, A D B C
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Angle between the internal bisectors of two angles of a triangle ∠B and ∠C is 120°, then ∠A is :
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G is the centroid of the equilateral ΔABC. If AB = 10 cm then length of AG is ?
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ABC is a right-angled triangle with AB = 6 cm and BC = 8 cm. A circle with center O has been inscribed inside ΔABC. The radius of the circle is
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A point D is taken on the side BC of a right-angled triangle ABC, where AB is hypotenuse. Then
A. AB2 + CD2 = AD2 + BC2
B. CD2 + BD2 = 2AD2
C. AB2 + AC2 = 2AD2
D. AB2 = AD2 + BC2
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ABC is an equilateral triangle and CD is the internal bisector of ∠C. If DC is produced to E such that AC = CE, then ∠CAE is equal to
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If each angle of a triangle is less than the sum of the other two, then the triangle is
A. Obtuse angled
B. Acute or equilateral
C. Acute angled
D. Equilateral
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In ΔABC and ΔDEF, AB = DE and BC = EF, then one can infer that ΔABC ≅ ΔDEF, when
A. ∠BAC = ∠EFD
B. ∠ACB = ∠EDF
C. ∠ABC = 2∠DEF
D. ∠ABC = ∠DEF
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In triangle ABC, ∠BAC = 75°, ∠ABC = 45°, B C 3 x
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The angles of a triangle are in the ratio 2 : 3 : 7. The measure of the smallest angle is :
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