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P lies on the circle with diameter AB exactly when AP^2 + BP^2 = AB^2

This type of question, asked 2 times: CDS 1 2019, CDS 2 2026. All 2 questions below, oldest first.

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  1. Question 1

    CDS 1 2019

    38
    A line segment ABAB is the diameter of a circle with centre at OO having radius 6.5 cm. Point PP is in the plane of the circle such that AP=xAP = x and BP=yBP = y. In which one of the following cases the point PP does not lie on the circle ?

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  2. Question 2

    CDS 2 2026

    65
    A Question is given followed by two Statements I and II. Consider the Question and the Statements and mark the correct option. Question : ABC is a triangle inscribed in a semi-circle such that AC coincides with the diameter of the semi-circle. Let P be any point on the arc of the semi-circle. What is AP2+CP2+AC2AP^2 + CP^2 + AC^2 equal to ? Statement I : The radius of the circle is 5 cm. Statement II : AB = 6 cm and BC = 8 cm. Which one of the following is correct in respect of the above Question and Statements ?

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