An isosceles triangle and an arc

HOME

Math Central

Quandaries & Queries

Question from Sreeharsha, a student:

The diagram shows an isosceles triangle ABC in which BC = AC = 20 cm, and angle BAC = 0.7
radians. DC is an arc of a circle, centre A. Find, correct to 1 decimal place,
(i) the area of the shaded region, [4]
(ii) the perimeter of the shaded region. [4]

This is question 10 from May/June 2004 University Of Cambridge International Examinations. I reproduced the diagram, added one pont E at the midpoint of AB and drew a line from C to E.

triangle

Angle AEC is a right angle. Can you see why? Use trigonometry to find the lengths of AE and EC. This should be enough information to allow you to complete the problem.

Write back if you need more assistance.

Penny

Math Central is supported by the University of Regina and the Imperial Oil Foundation.