Let the circumcentre of a triangle with vertices $A(a, 3)$, $B(b, 5)$ and $C(a, b)$, $ab > 0$ be $P(1, 1)$. If the line AP intersects the line BC at the point $Q(k_1, k_2)$, then $k_1 + k_2$ is equal to :

JEE Main 2022 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 29 July 2022, Shift 1, Maths Q13

Question 13 of 90 in this shift, Maths question 13 of 30, Section A.

Let the circumcentre of a triangle with vertices

A(a, 3)

B(b, 5)

and

C(a, b)

ab > 0

P(1, 1)

. If the line AP intersects the line BC at the point

Q(k_1, k_2)

, then

k_1 + k_2

is equal to :

(1) $2$
(2) $\frac{4}{7}$ Official answer
(3) $\frac{2}{7}$
(4) $4$

Official answer

Option 2

NTA final key.

Chapter: Straight Lines
Topic: Properties of Triangles
Idea tested: Inradius and Circumradius

Same idea in other shifts

Asked 6× in all

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Question text from the official JEE Main paper published by NTA; answer from the final answer key. Chapter, topic and idea tags, difficulty and skill are Lumi’s. Lumi analyses 108 of the 174 JEE Main shifts held from 2017 to 2026.