SSC (English Medium) १० वीं कक्षा - Maharashtra State Board Question Bank Solutions for Geometry Mathematics 2

If hypotenuse of a right angled triangle is 5 cm, find the radius of
the circle passing through all vertices of the triangle.

Choose the correct alternative: 

Out of the following which is a Pythagorean triplet? 

In ΔPQR, seg PM is a median, PM = 9 and PQ² + PR²  = 290. Find the length of QR. 

In ΔPQR, seg PM is the median. If PM = 9, PQ² + PR² = 290, Find QR. 

In ΔABC, seg AP is a median. If BC = 18, AB² + AC² = 260, then find the length of AP. 

Out of given triplets, which is not a Pythagoras triplet?

Out of given triplets, which is not a Pythagoras triplet?

Out of all numbers from given dates, which is a Pythagoras triplet?

Height and base of a right angled triangle are 24 cm and 18 cm. Find the length of its hypotenuse?

"The diagonals bisect each other at right angles." In which of the following quadrilaterals is the given property observed?

Which of the following figure is formed by joining the mid-points of the adjacent sides of a square?

In the given figure, triangle ABC is a right-angled at B. D is the mid-point of side BC. Prove that AC² = 4AD² – 3AB².

In the given figure, ∆QRS is an equilateral triangle. Prove that,

1. arc RS ≅ arc QS ≅ arc QR
2. m(arc QRS) = 240°.
   

In the given figure, chord AB ≅ chord CD, Prove that, arc AC ≅ arc BD.

In the given figure, in a circle with centre O, length of chord AB is equal to the radius of the circle. Find measure of each of the following.
(1) ∠ AOB (2)∠ ACB
(3) arc AB (4) arc ACB.

In a cyclic ▢ABCD, twice the measure of ∠A is thrice the measure of ∠C. Find the measure of ∠C?

Points A, B, C are on a circle, such that m(arc AB) = m(arc BC) = 120°. No point, except point B, is common to the arcs. Which is the type of ∆ABC?

`square`PQRS is a parallelogram. Write the sum of measures of ∠P and ∠ Q.