Chapter 13 Circle and Tangent Ex 13.2

RBSE Solutions for Class 10 Maths Chapter 13 Circle and Tangent

Class 10 Maths Chapter 13 Circle and Tangent Ex 13.2 Solution is provided in this post. Here we have provide the solutions of RBSE Boards Books according to chapter wise.

Rajasthan Board RBSE Class 10 Maths Chapter 13 Circle and Tangent Ex 13.2

Question 1.

According to figure, answer the following questions :

(i) ∠BAQ is an alternate segment of circle.

(ii) ∠DAP is an alternate segment of circle.

(iii) If C is joined with B, then ∠ACB is equal to which angle?

(iv) ∠ABD and ∠ADB is equal to which angles.

Solution :

(i) Alternate segment of ∠BAQ = ADB

(ii) Alternate segement of ∠DAP = ACBD

(iii) ∠ACB = ∠BAP

(iv) ∠ABD = ∠DAP and ∠ADB = ∠BAQ

Question 2.

According to figure, if ∠BAC = 80°, then find the value of ∠BCP.

Solution :

We know that

∵ Alternate segment of ∠BCP = ∠BAC

∴ ∠BCP = ∠BAC

⇒ ∠BCP = 80°

Question 3.

According to figure, PQ and XY are parallel tangents. If ∠QRT = 30°, then find the value of ∠TSY.

Solution :

Given :

PQ || XY

and ∠QRT = 30°

Diameter of circle of centre O is RS

∴ OR ⊥ PR and OS ⊥ XY

∴ ∠QRO = 90°

⇒ ∠QRS = 90°

∠RTS = ∠QRS – ∠QRT

= 90° – 30° = 60°

∴ ∠TRS = 60°

Now ∠TSY = ∠TRS

⇒ ∠TSY = 60°

Question 4.

Figure, in a cyclic quadrilateral ABCD diagonal AC bisects the angle C. Then prove that diagonal BD is parallel to tangent PQ of a circle which passes through the points A.

Solution :

Given :

∠ACD = ∠ACB

Now, we can see here

that ∠PAD = ∠ABD (∵ angle in the alternate segment)

similarly ∠QAB = ∠ADB

Also AB is a common arc. ADB and ACB are the angle in the same segment.

∴ ∠ADB = ∠ACD

similarly, ∠ABD = ∠ACD

By equation (i), we find that

∠PAD = ∠ADB (alternate interior angle)

∴ PQ || BD

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