Explanation

Mode = value that appears most often  

4 appears 3 times, more than any other number  

Last verified on 08-05-2026

Explanation

• A tangent is a straight line that touches a circle at only one point.
• This point is called the point of contact.
• Unlike a secant, it does not cut the circle at two points.

Last verified on 08-05-2026

Explanation

cotθ = 1/tanθ  

So tanθ × cotθ = tanθ × (1/tanθ) = 1  

Last verified on 08-05-2026

Explanation

cosθ = adjacent/hypotenuse = 12/13  

Use sin²θ + cos²θ = 1  

sin²θ = 1 - (12/13)² = 1 - 144/169 = 25/169  

sinθ = ±5/13  

If we assume θ is in quadrant I, then sinθ = 5/13  

Last verified on 08-05-2026

Explanation

Make b the same in both ratios:  

a : b = 4 : 5 = 12 : 15

b : c = 3 : 2 = 15 : 10

So a : b : c = 12 : 15 : 10

Therefore a : c = 12 : 10 = 6 : 5

Last verified on 07-05-2026

Explanation

Mean = (3 + 5 + 7 + 9 + 11) / 5 = 35 / 5 = 7  

Last verified on 07-05-2026

Explanation

• From a point outside a circle, exactly two tangents can be drawn.
• These tangents touch the circle at two distinct points.
• Both tangents are equal in length from the external point.

Last verified on 07-06-2026

Explanation

This is a Pythagorean trig identity:  

sec²θ = 1 + tan²θ

So sec²θ - tan²θ = 1

Last verified on 07-05-2026

Explanation

sinθ = 5/13 → right triangle with opposite = 5, hypotenuse = 13  

Adjacent = √(13² - 5²) = √(169 - 25) = √144 = 12  

tanθ = opposite/adjacent = 5/12  

Last verified on 07-05-2026

Explanation

• If two triangles have equal heights, their areas depend only on their bases.
• Area of triangle = ½ × base × height.
• With same height, the ratio of areas equals the ratio of their bases.

Last verified on 07-05-2026