81.

In a right-angled triangle, the product of two sides is equal to half of the square of the third side i.e. hypotenuse. One of the acute angles must be

• 60° 

• 30° 

• 45° 

• 45° 

If two concentric circles are of radii 5cm and 3cm, then the length of the chord of the larger circle which touches the smaller circle is

• 6 cm

• 7 cm

• 10 cm

• 10 cm

Inside a square ABCD, ΔBEC is an equilateral triangle. If CE and BD intersect at O. then ∠BOC is equal to

• 60° 

• 75° 

• 90° 

• 90° 

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

Let C be a point on a straight line AB. Circles are drawn with diameters AC and AB. Let P be any point on the circumference of the circle with diameter AB. If AP meets the other circle at Q, then

• QC || PB

• QC is never parallel to PB

• 
• 

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° = 

Each interior angle of a regular octagon in radians is

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°

If , then the value of  is