Points A, B and C lie on a circle. Point O is the center of the circle

Question

https://gmatclub.com/forum/download/file.php?id=27269 Points A, B and C lie on a circle. Point O is the center of the circle and lies on the straight line AB. AC = CB. AB = 18 inches. What is the area of triangle ABC? (Figure not drawn to scale.) A. 9 square inches B. 18 square inches C. 49 square inches D. 72 square inches E. 81 square inches Kudos for a correct solution . circle.gif

balamoon · Answer

Solution -

Given that AC = CB ----Isosceles triangle with diameter or base AB = 18 inches. OC is radius or height = AB/2 = 9 inches.

Area of triangle ABC = 1/2*AB*OC = 1/2*18*9 = 81 inches. ANS E.

ENGRTOMBA2018 · Answer

circle.gif Triangle ABC is a right angled triangle with right angle at C (from the fact that AB is the diameter and C is on the circumference and angle subtended by the diameter on the circumference is always 90 degrees). Also, AC=CB and AB =18 Thus, in the right triangle ABC, with \angle {ACB} = 90 , we have AB^2 = AC^2 + BC^2 ---> Let AC = x ---> 2x^2 = 18^2 --->x^2 / 2 = 324 / 4 = 81 in^2 . thus the area of the triangle is 81 sq. inches. E is the correct answer.

GMATinsight · Answer

Given : AC = CB

i.e. ABC is isosceles Right angle triangle therefore OC will be the Line of Symmetry and will be Perpendicular Bisector of AB

Also OC = OA = OB = Radius = AB/2 = 18/2 = 9

i.e. Area of triangle = (1/2)*AB*OC = (1/2)*(18)*(9) = 81

Answer: Option E

ashokk138 · Answer

Given AB = 18 inches which is the diameter. Since this is an isosceles triangle, CO is equal to the radius => 18/2 = 9 inches.

Area of Triangle = 1/2 * AB * CO = 1/2 * 18 * 9 = 81 square inches.

Option E.

Another way, we can draw a similar triangle at the bottom and assume it as a square with diagonal 18 inches, hence side = 9 \sqrt{2} 
Area of triangle = 1/2 * area of sq. = 1/2 * 9 \sqrt{2}  * 9 \sqrt{2}  = 81 square inches

jgcanada · Answer

Triangle inscribed in circle with hypo as diameter means it is right angle triangle.

AC=CB means it is isoc. triangle

1:1:root(2) ratio of sides

hypo = 18 => root(2) x root(2) x 9

plugging into ratio above we get

root(2) x 9 : root(2) x 9 : root(2) x root(2) x 9

formula for area of triangle: 1/2 x root(2) x 9 x root(2) x 9 = 9 x 9 = 81

Ans is E

Bunuel · Answer

800score Official Solution:

Point O is the center of the circle, so OA, OB, and OC are radii. AC = CB is given. Since their sides are equal, triangle AOC is congruent to triangle BOC. (AC = CB, OA = OB, OC = OC) Triangle AOC is congruent to triangle BOC, so angle AOC = angle BOC. Since
point O is on segment AB, angle AOC + angle BOC = 180 degrees. So each angle is equal to 90 degrees, and triangles AOC and BOC are right triangles.

Diameter AB = 18 inches, so a radius is 9 inches.
The area of triangle AOC is (1/2) × AO × OC = (1/2) × 9 × 9 = 81/2 square inches. The area of triangle BOC is also 81/2 square inches. The area of triangle ABC is the sum othe areas of triangles AOC and BOC, so it equals 81/2 + 81/2 = 81 square inches.

The correct answer is choice (E).

Abhinandan Dey · Answer

Here, 
AB is the Diameter and OC is the radius.
So, OC = AO = OB = Radius = 18/2 = 9 inches.
OC is also the height of triangle ABC.
So, Area of ABC triangle = 1/2 * AB * OC = 1/2 * 18 * 9 = 81 sq inches

Points A, B and C lie on a circle. Point O is the center of the circle

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

Points A, B and C lie on a circle. Point O is the center of the circle

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards