NCERT Solutions Class 9 Maths Chapter 10 – CIRCLES Exercise 10.5

Chapter 10 – CIRCLES Exercise 10.5

(Q 1) In Fig. 10.36, A,B and C are three points on a circle with centre O such that ∠BOC=30° and ∠AOB=60° If D is a point on the circle other than the arc ABC, find ∠ADC

Chapter 10 - CIRCLES Exercise 10.5

(Q 2) A chord of a circle is equal to the radius of the circle. Find the angle subtended by the chord at a point on the minor arc and also at a point on the major arc.

ANS

Chapter 10 - CIRCLES Exercise 10.5

(Q 3) In Fig. 10.37, ∠PQR = 100°, where P, Q and R are points on a circle with centre O. Find ∠OPR.

Ans

Chapter 10 - CIRCLES Exercise 10.5

(Q 4) In Fig. 10.38, ∠ABC = 69°, ∠ACB = 31°, find ∠BDC.

Ans

(Q 5) In Fig. 10.39, A, B, C and D are four points on a circle. AC and BD intersect at a point E such that ∠BEC = 130° and ∠ECD = 20°. Find ∠BAC.

Ans

Chapter 10 - CIRCLES Exercise 10.5

(Q 6) ABCD is a cyclic quadrilateral whose diagonals intersect at a point E. If ∠DBC = 70°, ∠BAC is 30°, find ∠BCD. Further, if AB = BC, find ∠ECD.

Chapter 10 - CIRCLES Exercise 10.5

(Q 7) If diagonals of a cyclic quadrilateral are diameters of the circle through the vertices of the quadrilateral, prove that it is a rectangle.

Ans

(Q 8) If the non-parallel sides of a trapezium are equal, prove that it is cyclic.

Ans

Chapter 10 - CIRCLES Exercise 10.5

(Q 9) Two circles intersect at two points B and C. Through B, two line segments ABD and PBQ are drawn to intersect the circles at A, D and P, Q respectively (see Fig. 10.40). Prove that ∠ACP = ∠QCD.

Ans

(Q 10) If circles are drawn taking two sides of a triangle as diameters, prove that the point of intersection of these circles lie on the third side.

Ans

Chapter 10 - CIRCLES Exercise 10.5

(Q 11) उभयनिष्ठ कर्ण AC वाले दो समकोण त्रिभुज ABC और ADC हैं। सिद्ध कीजिए कि ∠CAD=∠CBD है ।

Ans

Chapter 10 - CIRCLES Exercise 10.5

(Q 12) ABC and ADC are two right triangles with common hypotenuse AC. Prove that ∠CAD = ∠CBD.

Ans