JIPMAT 2021 (QA) - ABC is right angled triangle at C. Let BC = a, CA = b and AB = c and let p be the length of perpendicular from C on AB, then cp is equal to | PYQs + Solutions | AfterBoards
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JIPMAT 2021

Geometry
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Triangles

Conceptual

ABC is right angled triangle at C. Let BC = a, CA = b and AB = c and let p be the length of perpendicular from C on AB, then cp is equal to

Correct Option: 2
1) In right triangle ABC:\newline - BC = aa\newline - CA = bb\newline - AB = cc\newline - Perpendicular from C to AB = pp
2) Area of triangle can be written in two ways:\newline - Area = 12×base×height\frac{1}{2} × \text{base} × \text{height}\newline - Area = 12×product of sides containing right angle\frac{1}{2} × \text{product of sides containing right angle}
3) Using both formulas:\newline 12c×p=12a×b\frac{1}{2}c × p = \frac{1}{2}a × b
4) Therefore:\newline cp=abcp = ab
The answer is abab.
The key here is that the area of a right triangle equals half the product of either:\newline- Base and height (cp/2cp/2)\newline- Two sides forming right angle (ab/2ab/2)\newlineSince these are equal, cp=abcp = ab

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JIPMAT 2022

Given below are two statements:
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Statement II: In △ABC\triangle A B C, is an isosceles with AC=BCA C=B C. If AB2=2AC2A B^{2}=2 AC^{2}, Then angle C=90∘C=90^{\circ}
In the light of the above statement, choose the correct answer form the question below.

JIPMAT 2024

An equilateral triangle ABC\mathrm{ABC} is inscribed in a circle of radius 203 cm20 \sqrt{3} \mathrm{~cm}. What is the length of the side of the triangle ?

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An equilateral triangle ABCA B C is inscribed in a circle of radius 203 cm20 \sqrt{3} \mathrm{~cm}. The centroid of the triangle ABCA B C is at a distance dd from the vertex AA. then dd is equal to ?

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