5-Day Free Trial
5-day free, full-access trial TTP
Available with Beat the GMAT members only code
MORE DETAILS
Geometry
This topic has expert replies
-
Matt@VeritasPrep
- GMAT Instructor
- Posts: 2630
- Joined: Wed Sep 12, 2012 3:32 pm
- Location: East Bay all the way
- Thanked: 625 times
- Followed by:119 members
- GMAT Score:780
Any time you have an inscribed angle, you can draw a central angle to the same two points such that the central angle is DOUBLE the inscribed angle.
So if <AED = 75°, <AOD = 150° (where O is the center of the circle).
From there, <AOB, <BOC, and <COD sum up to 150° and are each the same, so
<AOB = <BOC = <COD = 50°.
∆BOC is isosceles (since two of the sides are the radius of the circle), so its angles are 50°, 65°, and 65°. x is two of the base angles, or 2*65° => 130°.
So if <AED = 75°, <AOD = 150° (where O is the center of the circle).
From there, <AOB, <BOC, and <COD sum up to 150° and are each the same, so
<AOB = <BOC = <COD = 50°.
∆BOC is isosceles (since two of the sides are the radius of the circle), so its angles are 50°, 65°, and 65°. x is two of the base angles, or 2*65° => 130°.
Matt@VeritasPrep wrote:Any time you have an inscribed angle, you can draw a central angle to the same two points such that the central angle is DOUBLE the inscribed angle.
So if <AED = 75°, <AOD = 150° (where O is the center of the circle).
From there, <AOB, <BOC, <COD sum up to 150° are each the same, so
<AOB = <BOC = <COD = 50°.
Dear Matt,
Just a small clarification,
All these angles are equal coz all of them (OAB,OBC,OCD) are congruent to each other via SSS congruence theorem. right ?
Regards
Teja
-
OptimusPrep
- Master | Next Rank: 500 Posts
- Posts: 410
- Joined: Fri Mar 13, 2015 3:36 am
- Location: Worldwide
- Thanked: 120 times
- Followed by:8 members
- GMAT Score:770
The angles are same because AB = BC = CA
Hence the angles subtended by these chords on the centre will also be same, as will be the arcs.
Does this help?
Hence the angles subtended by these chords on the centre will also be same, as will be the arcs.
Does this help?
Thank you sir ....yes sir it completely made sense....completely forgot this rule.OptimusPrep wrote:The angles are same because AB = BC = CA
Hence the angles subtended by these chords on the centre will also be same, as will be the arcs.
Does this help?
Regards
Teja
