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## Tamilnadu Samacheer Kalvi 9th Maths Solutions Chapter 4 Geometry Ex 4.4

Question 1.

Find the value of x in the given figure.

Solution:

In the cyclic quadrilateral ABCD

∠ABC = 180° – 120° = 60°

∠BCA = 90°

∴ x = ∠BAC = 180°- (90° + 60°) = 30°

Question 2.

In the given figure, AC is the diameter of the circle with centre O. If ∠ADE = 30°; ∠DAC = 35° and ∠CAB = 40°.

Find

(i) ∠ACD

(ii) ∠ACB

(iii) ∠DAE

Solution:

(i) ∠ACD = 180°- (90° + 35°) = 180°- 125° = 55°

(ii) ∠ACB = 180°- (90°+ 40°)= 180° – 130° = 50°

(iii) ∠ADC = 90°

∠CAE = 180° – 120° = 60°

∴ ∠DAE = 60°- 35° = 25°

Question 3.

Find all the angles of the given cyclic quadrilateral ABCD in the

Solution:

Question 4.

In the given figure, ABCD is a cyclic quadrilateral where diagonals intersects at P such that ∠DBC = 40° and ∠BAC = 60° find

(i) ∠CAD

(ii) ∠BCD

Solution:

Question 5.

In the given figure, AB and CD are the parallel chords of a circle with centre O. Such that AB = 8 cm and CD = 6 cm. If OM ⊥ AB and OL ⊥ CD distance between LM is 7 cm. Find the radius of the circle?

Solution:

In the figure LM = 7 cm

Question 6.

The arch of a bridge has dimensions as shown, where the arch measure 2 m at its highest point and its width is 6 m. What is the radius of the circle that contains the arch?

Solution:

Question 7.

In figure ∠ABC = 120°, where A,B and C are points on the circle with centre O. Find ∠OAC ?

Solution:

Question 8.

A school wants to conduct tree plantation programme. For this a teacher allotted a circle of radius 6 m ground to nineth standard students for planting sapplings. Four students plant trees at the points A, B, C and D as shown in figure. Here AB = 8 m, CD = 10 m and AB ⊥ CD. If another student places a flower pot at the point P, the intersection of AB and CD, then find the distance from the centre to P.

Solution:

ONPM is a rectangle with all the angles 90° and with length \(\sqrt{20}\) cm, breadth \(\sqrt{11}\) cm.

We need to find OP which is the diagonal of the rectangle ONPM.

Question 9.

In the given figure, ∠POQ = 100° and ∠PQR = 30°, then find ∠RPO.

Solution: