Question

Class 10th Maths 2
AB and AC are the two chords of the circle whose radius is 'r'. If p and q are the distance of called AB and CD from the centre respectively and if AB=2AC then prove that 4qsquare=p^2+3r^2​

Answer 1

Step-by-step explanation:

Given:

AB and AC are two chords of a circle with center O. Such that AB=2AC

p and q are ⊥ distances of AB and AC from center Oi.e., OM=p and ON=q

r is the radius of the circle

 

To prove that:

4q2=p2+3r2

 

Proof:

Join OA.

OM and ON are ⊥ distances of AB and AC from center O.

 

Here,

AN=2AC (perpendicular from center to chord intersect at mid-point of the chord)

AM=2AB (perpendicular from center to chord intersect at mid-point of the chord)

 

In right angled ΔOMA,

OM2+AM2=OA2

p2+AM2=r2

AM2=r2−p2       …… (1)

 

In right angled ΔONA,

ON2+AN2=OA2

q2+AN2=r2

AN2=