Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • NCERT
  • If circles are drawn taking two sides of a triangle as diameters, prove that the point of intersection of these circles lie on the third side.

Q 10. If circles are drawn taking two sides of a triangle as diameters, prove that the point of intersection of these circles lies on the third side.

Answers (1)

best_answer

Given: circles are drawn taking two sides of a triangle as diameters.

Construction: Join AD.

Proof: $A B$ is the diameter of the circle and $\angle A D B$ is formed in a semi-circle.
$\angle A D B=90^{\circ}$-------1 (angle in a semi-circle)
Similarly,
$A C$ is the diameter of the circle and $\angle A D C$ is formed in a semi-circle.
$\angle A D C=90^{\circ}$------2(angle in a semi-circle)
From 1 and 2, we have
$\angle \mathrm{ADB}+\angle \mathrm{ADC}=90^{\circ}+90^{\circ}=180^{\circ}$

$\angle A D B$ and $\angle A D C$ are forming a linear pair.

Hence, point D lies on this side.

Posted by

mansi

View full answer

Similar Questions

Trending Articles/News

anam-khan

CBSE Class 10 board exams twice a year ‘relief’ or ‘burden’? Parents, schools share mixed views
anam-khan

CBSE Class 10 exams twice a year from 2026; 64.4% students in favor, second attempt optional

Latest Question