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One side of a triangle and a rectangle is the same. The third vertex of the triangle lies on the midpoint of the rectangle side opposite the common side. The rectangle sides are in the ratio 2 : 3 and the common side is the longer side of the rectangle.  What is the sin value of the angle between the common side and the equal side of the triangle?
if A B C D and E are points in a plane such that the line CD bisects angle ACb and line CB bisects right angle ACE ,then DCE=?
The following questions have three statements. Study the question and the statements and decide which of the statement(s) is/are necessary to answer the question. Find the area of the isosceles triangle. I: The length of median to the side opposite to the single largest angle in the triangle is 3√5 cm. II: The length of the side opposite to the single largest angle in the triangle is 12 cm. III: The perimeter of the triangle is 30 cm.
In the given figure YZ bisects angle XYY' and YX bisects ∠ WXZ, then find the value of ∠ A'WX + ∠ YZX', if AA' || YY' || XX' '. 
The angle bisector bisects the angle exactly __________
Triangle XYZ is similar to triangle RST. Area of triangle XYZ is 2304 cm2 and area of triangle RST is 1296 cm2. If the longest side of the triangle XYZ measures 144 cm, then what will be the measure of the longest side of the triangle RST?
Three angles ∠P, ∠Q, and ∠R of a ∆PQR are 60°, 80°, and 40° respectively. The external angle bisector of ∠R meet at S with internal angle bisector of ∠Q and I is the incentre of ∆QRS, then what is the measure of ∠QIR?
Which of the following statements is/are true? A: If a chord of a circle bisects the radius of circle, then the angle formed by the chord at the center will be right angle. B: The shortest distance of a tangent from the center of a circle is equal to the radius of the circle. C: The circumcenter of a right-angled triangle is always on the hypotenuse of the triangle.
Statement 1: For calculating the minimum thickener area, the angle bisector method is used. Statement 2: In the angle bisector method, the point obtained the curve and the corresponding time is the time when the solids enter the compression zone.
The following questions are accompanied by three statements (I), (II) and (III). You have to determine which statement(s) is/are sufficient/necessary to answer the questions. Perpendicular and base of a right-angle triangle are 5x and 12x respectively. Find the area of right-angled triangle. I. Perimeter of the right-angle triangle is p cm.  II. Length of the diagonal side is d cm. III. Area of another triangle similar to given triangle is 300 cm2.