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

Explanation

Triangle rule: sum of any two sides must be > the third side.

7, 8, 9: 7+8 > 9, 7+9 > 8, 8+9 > 7 ✓

6, 7, 8: 6+7 > 8, 6+8 > 7, 7+8 > 6 ✓

5, 5, 6: 5+5 > 6, 5+6 > 5 ✓

5, 6, 11: 5+6 = 11, which is not > 11 ✗

Last verified on 07-06-2026