➛Ac is a diameter of a circle with center O. if ab and CD are two chords such that Ab is parallel to Cd. prove that AD = CD ?
[tex]:\pink\implies[/tex] Given :- BC is a diameter of a circle with centre O. AB and CD are two chords such that AB || CD.
➛To prove :- AB = CD
➛Construction :- Draw OL ⊥ AB and OM ⊥ CD.
➛Proof :-
In Δ OLB and Δ OMC, we have:
∠ OLB = ∠OMC [90° each]
∠ OBL = ∠ OCD [Alternate angles as AB || CD ]
OB = OC [Radii of a circle]
∴ Δ OLB ≅ Δ OMC (AAS criterion)
➛Thus, OL = OM (CPCT)
We know that chords equidistant from the centre are equal.
➛Hence, AB = CD
PᖇOᐺED !
Steps of Construction for an Angle of 45 °
[tex]i \: love \: you[/tex]
Copyright © 2024 EHUB.TIPS team's - All rights reserved.
Answers & Comments
[tex]\large\bold\pink{\underline{Question :-}}[\tex]
➛Ac is a diameter of a circle with center O. if ab and CD are two chords such that Ab is parallel to Cd. prove that AD = CD ?
[tex]:\pink\implies[/tex] Given :- BC is a diameter of a circle with centre O. AB and CD are two chords such that AB || CD.
➛To prove :- AB = CD
➛Construction :- Draw OL ⊥ AB and OM ⊥ CD.
➛Proof :-
In Δ OLB and Δ OMC, we have:
∠ OLB = ∠OMC [90° each]
∠ OBL = ∠ OCD [Alternate angles as AB || CD ]
OB = OC [Radii of a circle]
∴ Δ OLB ≅ Δ OMC (AAS criterion)
➛Thus, OL = OM (CPCT)
We know that chords equidistant from the centre are equal.
➛Hence, AB = CD
PᖇOᐺED !
Steps of Construction for an Angle of 45 °
3.) With A as the center, draw a line LA perpendicular to XY such that = 90°. ... Again with A as the center, taking any radius, draw an arc from the center A, cutting LA & AY at M & N respectively.
[tex]i \: love \: you[/tex]