In a circle with centre O, BC is a chord. Points D and A are on the circle, on the opposite side of BC, such that ∠DBC = 28° and BD = DC. What is the measure of ∠BOC?

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:

In ∆PQR, O is the incentre and ∠P = 42°. Then what is the measure of ∠QOR?

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:

In ∆ABC, ∠A=90⁰ , AD is the bisector of ∠A meeting BC at D, and DE ⊥ AC at E. if AB = 10 cm and AC = 15 cm, then the length of DE, in cm, is:

It is given that ∆ABC ≅ ∆PQR, AB = 5 cm, ∠B = 40°, and ∠A = 80°. Which of the following options is true?

PQRS is a cyclic quadrilateral. If ∠P is three times of ∠R and ∠S is four times of ∠Q, then the sum of ∠S + ∠R will be:

In a trapezium ABCD, AB and DC are parallel to each other with a perpendicular distance of 8 m between them. Also, (AD)=(BC)=10 m, and (AB) = 15 m <(DC). What is the perimeter (in m) of the trapezium ABCD?