41.

A point D is taken from the side BC of a right-angled triangle ABC, where AB is hypotenuse. Then

• AB² + CD² = BC² + AD²

• CD² + BD² = 2 AD²

• AB² + AC² = 2AD²

• AB² + AC² = 2AD²

An isosceles triangle ABC is right-angled at B. D is a point inside the triangle ABC. P and Q are the feet of the perpendiculars drawn from D on the sides AB and AC respectively of ΔABC. If AP = a cm, AQ = b cm and ∠BAD = 15°, sin 75° = 

D and E are two points on the sides AC and BC respectively of Δ ABC such that DE = 18 cm, CE = 5 cm and ∠DEC = 90°, If tan ∠ABC = 3.6, then AC : CD = 

• BC : 2 CE

• 2 CE : BC

• 2 BC : CE

• 2 BC : CE

 D is a point on the side BC of a triangle ABC such that . E is a point on AD for which AE : ED = 5 : 1. If  and then  then 

• 30°

• 45°

• 60°

• 40°

In ΔABC, P and Q are the middle points of the sides AB and AC respectively. R is a point on the segment PQ such that PR : RQ = 1 : 2. If PR = 2cm, the BC =  

• 4 cm

• 2 cm

• 12 cm

• 12 cm

The angles of a triangle are in Arithmetic Progression. The ratio of the least angle in degrees to the number of radians in the greatest angle is . The angles in degrees are

• 30°,  60°, 90°

• 35°, 55°, 90°

• 40°, 50°, 90°

• 40°, 50°, 90°

If the incentre of an equilateral triangle lies inside the triangle and its radius is 3 cm, then the side of the equilateral triangle is 

Suppose ΔABC be a right-angled triangle where  and  If Δ ABC = 40 cm², ΔACD = 10 cm² and  then the length of BC is

• 12 cm

• 18 cm

• 4 cm

• 4 cm

In ΔABC, D and E are points on AB and AC respectively such that DE || BC and DE divides the ΔABC into two parts of equal areas. Then ratio of AD and BD is

• 1 : 1

• 
• 
• 

I is the incentre of a triangle ABC. If  and  then the value of  is

• 130°

• 120°

• 140°

• 140°