CAT 2025 Lesson : Class Discussion: Geometry - Lines & Triangles: 9 to 16

Class Discussion – Lines and Triangles

Question 9

Consider obtuse-angled triangles with sides 8 cm, 15 cm and x cm. If x is an integer, then how many such triangles exist?
[CAT 2008]

		5
		21
		10
		15
		14

Question 10

In a triangle ABC, AB = 3, BC = 4 and CA = 5. Point D is the midpoint of AB, point E is on segment AC and point F is on segment BC. If AE = 1.5 and BF = 0.5, then

\angle

DEF =
[XAT 2008]

		$30\degree$
		$45\degree$
		$60\degree$
		$75\degree$
		Cannot be determined

Question 11

How many differently shaped triangles exist in which no two sides are of the same length, each side is of integral unit length and the perimeter of the triangle is less than 14 units?
[XAT 2009]

		3
		4
		5
		6
		None of the above

Question 12

A man standing on a boat south of a light house observes his shadow to be 24 metres long, as measured at the sea level. On sailing 300 metres eastwards, he finds his shadow as 30 metres long, measured in a similar manner. The height of the man is 6 metres above sea level.The height of the light house above the sea level is:
[XAT 2011]

		90 m
		94 m
		96 m
		100 m
		106 m

Question 13

A man standing on a boat south of a light house observes his shadow to be 24 metres long, as measured at the sea level. On sailing 300 metres eastwards, he finds his shadow as 30 metres long, measured in a similar manner. The height of the man is 6 metres above sea level.What is the horizontal distance of the man from the lighthouse in the second position?
[XAT 2011]

		300 m
		400 m
		500 m
		600 m
		None of the above

Question 14

The centre of a circle inside a triangle is at a distance of 625 cm. from each of the vertices of the triangle. If the diameter of the circle is 350 cm. and the circle is touching only two sides of the triangle, find the area of the triangle.
[XAT 2015]

		240000
		387072
		480000
		506447
		None of the above

Question 15

From a triangle ABC with sides of lengths 40 ft, 25 ft and 35 ft, a triangular portion GBC is cut off where G is the centroid of ABC. The area, in sq ft, of the remaining portion of triangle ABC is
[CAT 2017 S1]

		$225\sqrt{3}$
		$\dfrac{500}{\sqrt{3}}$
		$\dfrac{275}{\sqrt{3}}$
		$\dfrac{250}{\sqrt{3}}$

Question 16

Let ABC be a right-angled isosceles triangle with hypotenuse BC. Let BQC be a semi-circle, away from A, with diameter BC. Let BPC be an arc of a circle centered at A and lying between BC and BQC. If AB has length 6 cm then the area, in sq cm, of the region enclosed by BPC and BQC is
[CAT 2017 S1]

		$9\pi - 18$
		18
		$9\pi$
		9

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