AB is a chord of a circle in minor segment with center O.C is a point on the minorarc of the circle between the points A and B. The tangents to the circle at A and B meet at the point P. If ∠ACB = 102⁰ , then what is the measure of ∠APB?

if x+y =3 and $${1\over x}+{1\over y}= -{3\over 10}$$ then the value of (x²+y²) is :

Simplify the following expression.

$${\left({375+125} \right)^2-\left({125-375} \right)^2}\over 375×375-125×125$$

Find the value of

 sin⁴30⁰ + cos⁴30⁰ – sin25⁰cos65⁰-sin65⁰cos25⁰

The value of $$\left({sin37^0cos53^0+cos37^0sin^0} \right)-\left({4cos^237^0-7+4cos^253^0\over tan^247^0+4-cosec^243^0} is \right)$$

if x⁴+y⁴+x²y²=21 and x²+y²-xy=7, then what is the value of  $${x\over y}+{y\over x}=?$$

if 3sin²θ – cosθ-1=0, 0⁰< θ<90⁰, then what is the value of cot θ + cosec θ?

△ABC ∼ △DEF. If the areas of △ABC and △DEF are 100 cm² and 81 cm², respectively and the altitude of △DEF is 6.3 cm, then the corresponding altitude of △ABC is: