## EDGE- ANGLE -TEST-1

YKS Geometry threads angle-edge test-1

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Question 1) If point F in triangle ABC is the center of the inner tangent circle, [ED] parallel [BC], | EB | + | DC | = 12 cm; | AE | + | AD | What is the smallest integer value of cm?

Question 2) If triangle ABC is perpendicular to [AD] [BC], [AE] is central and its length is 16 cm, height is 12 cm; How many different integer values can the bisector length of the BAC angle take?

Question 3) ABC triangle, if the dimension of angle A is less than 90 °, | BP | = | PC |, | AB | = 6 cm, | AC | = 8 cm; How many cm is the integer value that | AP | = x can take?

Question 4) Triangle ABC, since the measure of angle A is greater than 90 °, the measure of angle B is greater than the measure of angle C, | BC | = 10 cm, | AC | = b, | AB | = c, b and c are integers; How many different values can C take?

Question 5) If ABC triangle, [AN] bisector, m (ACB) = m (PBA), | AP | = 11 cm, | BN | = 7 cm; How many integer values does | AB | = x have?

Question 6) ABC equilateral triangle, K; If a point inside the triangle is | EB | = 2 cm, | BD | = 5 cm, | AC | = 8 cm; | KE | + | KD | What is the largest integer value of cm?

Question 7) ABCD trapezoid, parallel to [AD] [BC], if the length of the bottom base is 4 times the length of the upper base, the length of the side edges is 6 cm and 8 cm; What is the largest integer value of the circumference of the trapezoid ABCD?

Question 8) ABC triangle, if the measure of angle A is greater than 90 °, | AD | = | AB |, | AC | = 10 cm, | BC | = 16 cm; How many integer values does | DC | = x have?

### EDGE TEST-1 SOLUTIONS

Solution: Since the point F in ABC triangle is the center of the inner tangent circle, [BF] is the bisector [CF]. | DC | = x is | EB | = 12-x. From inside opposite angles m (FCB) = m (CFD), m ( Since CBF) = m (EFB), | DF | = x, | EF | = 12-x. | ED | = 12 cm. In a triangle, the sum of the two side lengths is greater than the length of one side. | AE | + | Since ED | will be larger than 12 cm, the smallest integer value is 13 cm.

Solution: In a triangle ABC, the height of the base, the bisector, the median are respectively ha, na, Va and | AB | | AC | Unlike from, ha <na <Va. In triangle ABC, since the triangle inequality is 12 <x <16, the bisector length can take 3 different integer values.

Solution: Let [PK] be parallel to [AB] in triangle ABC. | AK | = | KC | = 4 cm, | KP | = 3 cm. In triangle APK, 1 <x <7 from triangle inequality. The measure of angle A is the angle AKP. The AKP angle is greater than 90 ° since it is integral with its size. So 4² + 3² <x², 5

Solution: Since the dimension of angle A is greater than 90 °, it is 10² <b² + c², since the measure of angle B is greater than the measurement of angle C, c <b, c² <b². If the inequalities are added to the side, 10² <2b², root50

Solution: Let m (BAN) = m (NAC) = a, m (ACN) = m (PBA) = b, m (NBP) = c.m (BPN) = m (PNB) = a + b (outer angle ), | BP | = | BN | = 7 cm. The ABP triangle inequality is 4 <x <18.

Solution: Since ABC is an equilateral triangle, | AE | = 6 cm, | DC | = 3 cm. From the cosine theorem in ADC triangle | AD | ² = 8² + 3²-2.8.3.cos60 °, | AD | = 7 cm. KE | + | KD | <| AE | + | AD |, | KE | + | KD | <13, | KE | + | KD | The largest integer value that can take is 12 cm.

Solution: Let [AE] be parallel to [DC]. Since AECD is parallelogram, | AD | = | EC | = x cm, | AE | = | DC | = 9 cm. In triangle ABE, (4/3) <x The circumference of the cotton ABCD is 14 + 5x. The maximum value of the circumference (ABCD) will be 14 + 5. (14 /) 3 = 112/3, so the integer value is 37 cm.

Solution: Since the dimension of angle A in triangle ABC is greater than 90 °, y² <156, from triangle inequality 6x²> 139. Accordingly, the integer value of x is 12 cm.