# I have drawn a ri

Given: ABC is a right angled triangle with A = 90°

To prove: BQ2 + PC2 = BC2 + PQ2

Proof:

By applying Pythagoras theorem in ΔAPQ, we get,

PQ2 = AP2 + AQ2 ……………… (1)

By applying Pythagoras theorem in ΔABQ, we get,

BQ2 = AB2 + AQ2 ……………… (2)

By applying Pythagoras theorem in ΔAPC, we get,

PC2 = AP2 + AC2 ………………… (3)

By applying Pythagoras theorem in ΔABC, we get,

BC2 = AB2 + AC2 ……………… (4)

By adding (1) and (2) we get,

BQ2 + PC2 = AB2 + AQ2 + AP2 + AC2

BQ2 + PC2 = AB2 + AC2 + AQ2 + AP2

Substituting from (1) and (4) we get,

BQ2 + PC2 = BC2 + PQ2

Hence proved.

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses
RELATED QUESTIONS :

A person goes 24mWest Bengal Board - Mathematics

Two rods of 13m. West Bengal Board - Mathematics

In ΔABC, if AB = West Bengal Board - Mathematics

If the lengths ofWest Bengal Board - Mathematics

In the adjoining West Bengal Board - Mathematics

I have drawn a trWest Bengal Board - Mathematics

Let us fill in blWest Bengal Board - Mathematics

In ΔRST, <span laWest Bengal Board - Mathematics

The point O is siWest Bengal Board - Mathematics

ABC is and isosceWest Bengal Board - Mathematics