In ∆ABC, ∠C=90⁰, Point P and Q are on the sides AC and BC, respectively, such that  AP:PC=BQ:QC=1:2.Then, $${AQ^2+BP^2}\over AB^2$$  is equal to:

Let ABC be an equilateral triangle and AX, BY, CZ be the altitudes. Then the right statement out of the four given responses is

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

In ∆ABC, the bisector of ∠A intersects side BC at D. If AB = 12 cm, AC = 15 cm and BC= 18 cm, then the length of BD is:

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?

ABC is an isosceles triangle such that AB = AC and ∠B = 35°. AD is the median to the base BC. Then ∠BAD is

If ABC is an equilateral triangle and D is a point on BC such that AD⊥BC, then 

Point P lies outside a circle with centre O. Tangents PA and PB are drawn to meet the circle at A and respectively. If ∠APB =80⁰, then ∠OAB is is equal to: