# Triangles and Circles (IMO- Mathematics Olympiad (SOF) Class 9): Questions 44 - 47 of 79

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## Question number: 44

» Triangles and Circles

MCQ▾

### Question

In triangle ABC, the altitude from A to BC meets BC at D, and the altitude from B to CA meets AD at H. if , and , if then the length of HD is ________

### Choices

Choice (4) Response

a.

b.

c.

d.

## Question number: 45

» Triangles and Circles

MCQ▾

### Question

A1 is a circle of radius 8 cm, A2 is a circle of radius 12 cm. Shivangi wants the two circles to touch tangentially. She knows that there are two possibilities for the distance between their centres. What are these two distances?

### Choices

Choice (4) Response

a.

5 cm and 19 cm

b.

4 cm and 20 cm

c.

16 cm and 8 cm

d.

12 cm and 4 cm

## Question number: 46

» Triangles and Circles

MCQ▾

### Question

Triangle PAB is formed by three tangents to circle with center O and, then angle AOB equals ________

### Choices

Choice (4) Response

a.

b.

c.

d.

## Question number: 47

» Triangles and Circles

MCQ▾

### Question

A, B, C and D are four points on a circle. AC and BD intersect at a point E such that and, then angle is ________

### Choices

Choice (4) Response

a.

b.

c.

d.

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